Aalborg Universitet

Review of Laterally Loaded Monopiles Employed as the Foundation for Offshore WindTurbines

Sørensen, Søren Peder Hyldal; Brødbæk, Kristian Thoustrup; Møller, Martin; Augustesen,Anders Hust

Publication date:2012

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Citation for published version (APA):Sørensen, S. P. H., Brødbæk, K. T., Møller, M., & Augustesen, A. H. (2012). Review of Laterally LoadedMonopiles Employed as the Foundation for Offshore Wind Turbines. Department of Civil Engineering, AalborgUniversity. DCE Technical reports No. 137

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ISSN 1901-726X DCE Technical Report No. 137

Review of laterally loaded mono-

piles employed as the foundation

for offshore wind turbines

Søren Peder Hyldal SørensenKristian Thoustrup Brødbæk

Martin Møller

Anders Hust Augustesen

Department of Civil Engineering

DCE Technical Report No. 137

Review of laterally loaded monopiles employed

as the foundation for offshore wind turbines

by

Søren Peder Hyldal Sørensen Kristian Thoustrup Brødbæk

Martin Møller Anders Hust Augustesen

Aalborg University Department of Civil Engineering

Geotechnical Engineering Research Group

February 2012

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Published 2012 by

Aalborg University

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Printed in Aalborg at Aalborg University

ISSN 1901-726X

DCE Technical Report No. 137

Review of laterally loaded monopiles employed asthe foundation for o�shore wind turbinesS. P. H. Sørensen1;K. T. Brødbæk2; M. Møller2; and A. H. Augustesen3Aalborg University, February 2012Abstra tThe monopiles foundation on ept is often employed as the foundation for o�shorewind turbine onverters. These piles are highly subje ted to lateral loads andoverturning moments due to wind and wave for es. Typi ally monopiles withdiameters of 4 to 6 m and embedded pile lengths of 15 to 30 m are ne essary. In urrent pra ti e these piles are normally designed by use of the p�y urve methodalthough the method is developed and veri�ed for small-diameter, slender piles. Inthe present paper a review of the existing p�y urve formulations for piles in sand ispresented. Based on numeri al and experimental studies presented in the literature,advan es and limitations of the urrent p�y urve formulations are outlined. The re-view fo uses on the design of monopile foundations for o�shore wind turbine onverters.1 Introdu tionIt is a predominating opinion that theglobal warming is aused by the emissionof greenhouse gasses. Therefore, it is ofhigh politi al interest to redu e the emis-sion of greenhouse gasses. This an bea omblished by investments in renewableenergy. Wind power is a very ompeti-tive sour e of renewable energy, and there-fore the market for both onshore and o�-shore wind farms is expe ted to expand.In 2008, the wind energy apa ity in theworld was approximately 120 GW of whi hEurope a ounted for 65 GW. In 2030,the wind energy apa ity in Europe is ex-pe ted to rea h 400 GW orresponding toan in rease of 515 % ompared to the a-pa ity in 2008. Currently, the majority1M. S ., Ph.D. Student in Civil Engineering,Dept. of Civil Engineering, Aalborg University,Sohngaardsholmsvej 57, 9000 Aalborg, Denmark.2M. S . in Civil Engineering, COWI A/S3M. S ., Ph.D. in Civil Engineering, COWIA/S

of wind turbines are pla ed onshore dueto lower onstru tion osts onshore thano�shore. However, dense populations andbuilt-up areas limit the number of suitablelo ations on land. Therefore, the develop-ment of o�shore wind farms are enfor ed.In 2011, the o�shore wind energy apa -ity in Europe was approximately 4 GW,while the apa ity in 2030 is expe ted toin rease to approximately 150 GW. (seewww.ewea.org)Several on epts for o�shore wind turbinefoundations exist, for instan e, monopilefoundations, gravitational foundations,bu ket foundations, tripods, ja ket foun-dations, and �oating foundation on epts.The hoi e of foundation on ept primar-ily depends on site onditions and thedominant type of loading. At moderatewater depths the most ommon founda-tion prin iple is monopiles, whi h are sin-gle steel pipe piles driven open-ended intothe soil. A ording to LeBlan et al.(2009) monopiles installed re ently have5

6diameters around 4 to 6 m and a pile slen-derness ratio, L/D, around 5 where L isthe embedded pile length and D is theouter pile diameter.For o�shore wind turbine foundations theservi eability and fatigue limit states areoften governing for the design. The foun-dations should be designed su h that thea umulated rotation is less than the re-quirements of the wind turbine produ er.Often the rotation due to installation isnot allowed to ex eed 0.25◦ and the a u-mulated rotation due to loads is restri tedto 0.25◦. Furthermore, the foundationshould be designed su h that resonan ewith the rotor frequen y, the blade passingfrequen y, and the energy ri h frequen y ofthe environmental loads is avoided. Hen e,the sti�ness of the foundation for o�shorewind turbines is of great importan e. Theblade passing frequen y and the rotor fre-quen y of the wind turbine are typi allyin the range of 0.5-1.0 and 0.17-0.33 Hz,respe tively. Monopile foundations for o�-shore wind turbines are typi ally designedsu h that the �rst natural frequen y of thestru ture is between the blade passing fre-quen y and the rotor frequen y.In urrent design of laterally loaded o�-shore monopiles, the winkler model ap-proa h is normally used. Further, p�y urves are typi ally used to des ribe theintera tion between pile and soil. A p�y urve des ribes the non-linear relationshipbetween the soil resistan e a ting againstthe pile wall, p, and the lateral de�e -tion of the pile, y. Note that there in thepresent paper is distinguished between soilresistan e, p, and ultimate soil resistan e,pu. The soil resistan e is given as the re-a tion for e per unit length a ting on thepile. The ultimate soil resistan e is givenas the maximum value of soil resistan e.Several formulations of p�y urves existdepending on the type of soil. These for-mulations are originally formulated to beemployed in the o�shore oil and gas se -

tor. However, they are also used for o�-shore wind turbine foundations, althoughpiles with signi� antly larger diameter andsigni� antly smaller slenderness ratio areemployed for the foundation of these.In the present paper the formulation andimplementation of p�y urves for piles insands proposed by Reese et al. (1974),O'Neill and Mur hison (1983), and designregulations of organs su h as the Ameri- an Petroleum Institute and Det NorskeVeritas API (API, 2000; and DNV, 2010)will be presented and analysed. However,alternative methods for designing laterallyloaded piles have been proposed in the lit-erature. Alternative approa hes an gen-erally be lassi�ed as follows:� The limit state method.� The subgrade rea tion method.� The elasti ity method.� The strain-wedge method.� The �nite element/di�eren e method.� Model testsSimplest of all the methods are the limitstate methods onsidering only the ulti-mate soil resistan e (e.g. Hansen, 1961;Broms, 1964; Petrasovits and Award,1972; Meyerhof et al., 1981; Prasad andChari, 1999; and Zhang et al., 2005).The simplest method for predi ting thepile de�e tion is the subgrade rea tionmethod, e.g. Reese and Matlo k (1956)and Matlo k and Reese (1960). In this ase the soil resistan e is assumed linearlydependent on the pile de�e tion. Small-and full-s ale tests though substantiate anon-linear relationship between soil resis-tan e and pile de�e tion. The subgraderea tion method must therefore be onsid-ered too simple and highly ina urate. Inaddition the subgrade rea tion method is

7not able to predi t the ultimate lateral pileresistan e.The p�y urve method assumes a non-linear dependen y between soil resistan eand pile de�e tion and is therefore able toprodu e a more a urate solution. In boththe p�y urve method and the subgrade re-a tion method the Winkler approa h, f.se tion 2, is employed to al ulate the lat-eral de�e tion of the pile and the inter-nal for es in the pile. When employingthe Winkler approa h the pile is onsid-ered as a beam on an elasti foundation.The beam is supported by a number of un- oupled springs with spring sti�ness' givenby p�y urves. When using the Winklerapproa h the soil ontinuity is not takeninto a ount as the springs are onsideredun oupled.The elasti ity method, e.g. Banerjee andDavis (1978), Poulos (1971), and Pou-los and Davis (1980), in ludes the soil ontinuity. However, the response is as-sumed to be elasti . As soil is more likelyto behave elasto-plasti ally, this elasti itymethod is not to be preferred unless onlysmall strains are onsidered. Hen e, themethod is only valid for small strains andthereby not valid for al ulating the ulti-mate lateral pile resistan e.The strain-wedge method was originallyproposed by Norris (1986) and was orig-inally able to predi t the respons of �exi-ble piles exhibited to lateral loading. Sin ethen, the model has been developed fur-ther by, for instan e, Ashour et al. (1998)and Ashour and Norris (2003) su h thatit an a ount for, among others, layeredsoils and soil liguefa tion. The strain-wedge method links the traditional Win-kler approa h with the three-dimensionalbehaviour of soils determined from triaxialtests.Another way to deal with the soil on-tinuity and the non-linear behaviour isto apply a three-dimensional �nite ele-ment/di�eren e model (e.g. Abdel-

Rahman and A hmus, 2005; Fan andLong, 2005; Lesny and Wiemann, 2006;Sørensen et al., 2009; Lin et al., 2010;and Sørensen et al., 2010). When apply-ing a three-dimensional numeri al modelboth deformations and the ultimate lat-eral resistan e an be determined. Dueto the omplexity of a three-dimensionalmodel, substantial omputational poweris needed and al ulations are often verytime onsuming. Phenomena su h as liq-uefa tion and gaps between soil and pileare at present hard to handle in the mod-els. Hen e, anumeri al modelling is a use-ful tool but the a ura y of the results ishighly dependent on the applied onstitu-tive soil models as well as the alibrationof these models.Model tests an be ondu ted to inves-tigate the behaviour of laterally loadedpiles. Model tests at large s ale are veryexpensive. Hen e, small-s ale tests are of-ten preferred. When ondu ting small-s ale tests at normal stress level, the fri -tion angle of the soil is high and Young'smodulus of elasti ity is low ompared tothe soil properties for full-s ale tests. Toover ome this issue, small-s ale tests anbe ondu ted in either a entrifuge orin a pressure tank in whi h an overbur-den pressure an be applied to the soil.Small-s ale tests have been ondu ted by,for instan e, Barton et al. (1983), Geor-giadis et al. (1992), Verdue et al. (2003),Sørensen et al. (2009), LeBlan et al.(2010a), LeBlan et al. (2010b), Klinkvortand Hededal (2010), and Brødbæk et al.(2011). When ondu ting small-s ale testsappropriate s aling laws are ne essary forthe s aling to full-s ale. S aling laws ap-pli able for laterally loaded piles have beenproposed by several authors (e.g. Gudehusand Hettler, 1983; Peralta and A hmus,2010; Leblan et al., 2010a; and Bhat-ta harya et al., 2011).In this paper the Winkler model approa hand the p�y urves proposed by Reese etal. (1974) and Mur hison and O'Neill

8(1984) are presented in detail. These p�y urves are valid for piles situated in ohe-sionless soil materials. The limitations ofthe Winkler model approa h and the p�y urves are dis ussed. Further, resear hwithin the �eld of laterally loaded pilessituated in sand is presented. The paperadresses monopile foundations for o�shorewind turbines.2 p�y urves and Winklerapproa hAs a onsequen e of the oil and gas in-dustry's expansion in o�shore platforms inthe 1950s, models for designing laterallyloaded piles were required. The key prob-lem is the soil-stru ture intera tion as thesti�ness parameters of the pile, Ep, andthe soil, Es, may be well known but at thesoil-pile interfa e the ombined parameterEpy is governing and unknown. In orderto investigate the soil-pile intera tion, anumber of �eld tests on fully instrumented�exible piles have been ondu ted and var-ious expressions for various soil onditionshave been derived to predi t the soil pres-sure a ting on a pile subje ted to lateralloading.Histori ally, the derivation of the p�y urve method for piles in sand is as fol-lows:� Analysing the response of beams onan elasti foundation, the soil is hara terised by a series of linear-elasti un oupled springs, introdu edby Winkler (1867).� Hetenyi (1946) presents a solution tothe beam on elasti foundation prob-lem.� M Clelland and Fo ht (1958) as wellas Reese and Matlo k (1956) suggestthe basi prin iples in the p�y urvemethod.

� Investigations by Matlo k (1970) in-di ates that the soil resistan e in onepoint is independent of the pile defor-mation above and below that exa tpoint.� Tests on fully instrumented test pilesin sand installed at Mustang Islandare arried out in 1966 and reportedby Cox et al. (1974).� A semi-empiri al p�y urve expressionis derived based on the Mustang Is-land tests, f. Reese et al. (1974).The expression be omes the state-of-the-art in the following years.� O'Neill and Mur hison proposes anew p�y urve formulation with a tan-gent hyperboli shape.� Mur hison and O'Neill (1984) om-pare the p�y urve formulations pro-posed by Reese et al. (1974), withthe expression by O'Neill and Mur hi-son (1983) and two simpli�ed ex-pressions (also based on the Mus-tang Island tests) by testing the for-mulations against a database of rel-atively well-do umented lateral pileload tests. The formulation of O'Neilland Mur hison (1983) was found toprovide better results ompared tothe original expressions formulated byReese et al. (1974). The expres-sion of O'Neill and Mur hison (1983)was later adopted by design regula-tions of organs su h as the Ameri anPetroleum Institute (API) and DetNorske Veritas (DNV).Resear h has been on entrated on deriv-ing empiri al (e.g. Reese et al. 1974)and �analyti al� (e.g. Ashour et al. 1998)p�y urve formulations for di�erent typesof soil giving the soil resistan e, p, as afun tion of pile displa ement, y, at a givenpoint along the pile. The soil pressure ata given depth, xt, before and during an

9ex itation is sket hed in �g. 1b. The pas-sive pressure on the front of the pile is in- reased as the pile is de�e ted the distan eyt while the a tive pressure at the ba k isde reased.

(a) Pile bending dueto lateral loading.(b) Stresses on a pile before and dur-ing lateral ex itation.Figure 1: Distribution of stresses before and dur-ing lateral ex itation of a ir ular pile. pt denotesthe net for e a ting on the pile at the depth xt,after Reese and Van Impe (2001).An example of a typi al p�y urve is shownin �g. 2a. The urve has an upper hori-zontal limit denoted by the ultimate soilresistan e, pu. The horizontal line impliesthat the soil has an ideal plasti behaviourmeaning that no loss of shear strength o - urs with in reasing strain. The subgraderea tion modulus, Epy, at a given depth, x,is de�ned as the se ant modulus p/y. Epyis thereby a fun tion of both lateral pilede�e tion, y, depth, x, as well as the phys-i al properties and load onditions. Epydoes not uniquely represent a soil prop-erty, but is simply a onvenient parame-ter that des ribes the soil-pile intera tion.

Epy de reases with in reased de�e tion, f.�g. 2b. A further examination of theshape of p�y urves is to be found in se -tion 3.Sin e the soil-pile intera tion is three-dimensional and highly nonlinear a sim-pli�ed and onvenient way to obtain the

(a) p�y urve.(b) Variation of subgrade re-a tion modulus.Figure 2: Typi al p�y urve and variation ofthe modulus of subgrade rea tion at a given pointalong the pile, after Reese and Van Impe (2001).soil resistan e along the pile is to applythe Winkler approa h in whi h the soilresistan e is modelled as un oupled non-linear springs with sti�ness Epy a ting onan elasti beam as shown in �g. 3. Byemploying un oupled springs layered soils an onveniently be modelled.

Figure 3: The Winkler approa h with the pilemodelled as an elasti beam supported by non-linear un oupled springs.The governing equation for beam de�e -tion was stated by Timoshenko (1941).The equation for an in�nitesimal small ele-ment, dx, lo ated at depth x, subje ted tolateral loading, an be derived from stati equilibrium. The sign onvention in �g. 4is employed. N , V , and M de�nes the ax-ial for e, shear for e and bending moment

10in the pile, respe tively. The axial for e,N , is assumed to a t in the ross-se tion's entre of gravity.Equilibrium of moments and di�erentiat-ing with respe t to x leads to the followingequation where se ond order terms havebeen negle ted:

d2M

dx2+

dV

dx−N

d2y

dx2= 0 (1)Following relations are used:

M = EpIpκ (2)dV

dx= −p (3)

p(y) = −Epyy (4)Ep and Ip are the Young's modulus of elas-ti ity of the pile and the se ond momentof inertia of the pile, respe tively. κ is the urvature strain of the beam element.

Figure 4: Sign onvention for in�nitesimal beamelement.With use of (2)�(4) and the kinemati as-sumption κ = d2ydx2 whi h is assumed inBernoulli-Euler beam theory the govern-ing fourth-order di�erential equation fordetermination of de�e tion is obtained:

EpIpd4y

dx4−N

d2y

dx2+ Epyy = 0 (5)In (5) the shear strain, γ, in the beam isnegle ted. This assumption is only validfor relatively slender beams. For short andrigid beams the Timoshenko beam theory,that takes the shear strain into a ount,

is preferable. The following relations areused:V = GpAvγ (6)γ =

dy

dx− ω (7)

κ =dω

dx(8)

Gp and Av are the shear modulus and thee�e tive shear area of the beam, respe -tively. ω is the ross-se tional rotation asde�ned in �g. 5. In Timoshenko beam the-ory the shear strain and hereby the shearstress is assumed to be onstant over the ross se tion. However, in reality the shearstress varies paraboli over the ross se -tion. The e�e tive shear area is de�nedso the two stress variations give the sameshear for e. For a pipe the e�e tive sheararea an be al ulated as:Av = 2(D − t)t (9)where t is the wall thi kness of the pipe.

Figure 5: Shear and urvature deformation of abeam element.By ombining (1)�(4) and (6)�(8) two ou-pled di�erential equations an be formu-lated to des ribe the de�e tion of the Tim-oshenko beam:GAv

d

dx

(

dy

dx− ω

)

− Epyy = 0 (10)EpIp

d3ω

dx3−N

d2y

dx2+ Epyy = 0 (11)In the derivation of the di�erential equa-tions the following assumptions have beenused:

11� The beam is straight and has a uni-form ross se tion.� The beam has a longitudinal plane ofsymmetry, in whi h loads and rea -tions lie.� The beam material is homogeneous,isotopi , and elasti . Furthermore,plasti hinges do not o ur in thebeam.� Young's modulus of elasti ity of thebeam material is similar in tensionand ompression.� Beam de�e tions are small.� The beam is not subje ted to dynami loading.3 Formulations of p�y urves for piles in sandp�y urves des ribing the stati and y li behaviour of piles in ohesionless soils arepresented followed by a dis ussion of theirvalidity and limitations, f. se tion 4.Only the formulation made by Reese etal. (1974), hereafter denoted Method A,and the formulation proposed by O'Neilland Mur hison (1983) and implemented indesign regulations su h as API (2000) andDNV (2010), Method B, will be des ribed.Both p�y urve formulations are empiri- ally derived based on full-s ale tests onfree-ended piles at Mustang Island.3.1 Full-s ale tests at MustangIslandTests on two fully instrumented, identi alpiles lo ated at Mustang Island, Texas asdes ribed by Cox et al. (1974), are thestarting point for the formulation of p�y urves for piles in sand. The test setup isshown in �g. 6 and 7.

To install the test- and rea tion piles aDelmag-12 diesel hammer was used. Thetest piles were steel pipe piles with diame-ters of D = 0.61 m (24 in) and wall thi k-nesses of wt = 9.5 mm (3/8 in). Theembedded length of the piles were 21.0m (69 ft) whi h orresponds to a slen-derness ratio of L/D = 34.4. The pileswere instrumented with a total of 34 a tivestrain gauges mounted from 0.3 m abovethe mudline to 9.5 m (32 ft) below themudline. The strain gauges were bondeddire tly to the inside of the pile in 17 levelswith highest on entration of gauges nearthe mudline. The horizontal distan e be-tween the entre of the two test piles was7.5 m (24 ft and 8 in), f. �g. 7. Betweenthe piles the load ell was installed on fourrea tion piles. The minimum horizontaldistan e from the entre of a rea tion pileto the entre of a test pile was 2.8 m (9ft and 4 in). Hen e, from ea h test pile,two rea tion piles were pla ed ea h withan angle of approximately 28◦ from the di-re tion of loading. Hen e, the total enterto enter distan e from ea h test pile tothe nearest rea tion piles were 3.2 m or-responding to 5.2D. A ording to Remaudet al. (1998), a trailing pile positioned re-spe tively 4D and 6D away from the lead-ing pile has in general a redu tion in sti�-ness and apa ity of 18 and 7 %, respe -tively. Therefore, a minor e�e t from therea tion piles must be expe ted. NeitherCox et al. (1974) nor Reese et al. (1974)mentions whether they a ount for groupe�e ts in the analysis of the pile tests.Prior to pile installation, two soil boringswere made, ea h in a range of 3.0 m (10 ft)from a test pile. The soil samples showeda slight di�eren e between the two areaswhere the piles were installed, as one bor-ing ontained �ne sand in the top 12 m(40 ft) and the other ontained silty �nesand. The strength parameters were de-rived from standard penetration tests a - ording to Pe k et al. (1953). The stan-dard penetration tests showed large varia-tions in the number of blows per ft. Espe-

12

Figure 6: Plan drawing of the test setup for the Mustang Island tests, after Cox et al. (1974). Measuresin meter.

Elev

ation

[m

]

2.7

0.90.30.0

8.89.5

21.0

Instr

umen

ted

secti

on

2.8 1.9 2.8Horizontal distance [m]

Load arrangement

Pile 1 Pile 2

Reaction piles

Diaphragm

Steel Pipe Pile :Outside diameter = 0.61 mWall thickness = 9.525 mmEmbedment length = 21 mEpIp = 1.7144 x 105 kNm2Figure 7: Cross-se tional view of the test setup for the Mustang Island tests, after Cox et al. (1974).

13 ially in the top 12 m (40 ft) of both bor-ings the number of blows per 30 m variedfrom 10 to 80. From 12 to 15 m (40 to 50ft) beneath the mudline lay was en oun-tered. Beneath the lay layer the strengthin reased from 40 to 110 blows per 30 m.From 18 m (60 ft) beneath the mudline tothe total depth the number of blows per30 m de reased from 110 to 15. The wa-ter table was lo ated at the soil surfa e,implying fully saturated soil.The piles were in total subje ted to sevenhorizontal load ases onsisting of two sta-ti and �ve y li . Pile 1 was at �rst sub-je ted to a stati load test 16 days afterinstallation. The load was applied in in- rements until a maximum load of 267 kN(60000 lb) was rea hed. The maximumload was determined as no failure o urredin the pile. After the stati load test onpile 1 two y li load tests were ondu tedwith varying load amplitude. A maximumof 25 load y les were applied. 52 daysafter installation a pull-out test was on-du ted on pile 2. A maximum of 1780 kN(400000 lb) was applied ausing the pile tomove 25 mm (1 in h). After another weekpile 2 was subje ted to three ases of y li loading and �nally a stati load test. Forthe y li loading a maximum of 100 load y les were applied. The stati load aseon pile 2 was performed immediately afterthe third y li load ase whi h might af-fe t the results. Reese et al. (1974) do not larify whether this e�e t is onsidered inthe analyses.3.2 Method AMethod A is the original method based onthe Mustang Island tests, f. Reese et al.(1974). The p�y urve formulation on-sists of three urves: an initial straightline, p1, a parabola, p2, and a straight line,p3, all assembled to one ontinuous pie e-wise di�erentiable urve, f. �g. 8. Thelast straight line from (ym,pm) to (yu,pu)

is bounded by an upper limit hara terisedby the ultimate soil resistan e, pu.Figure 8: p�y urve for stati loading usingmethod A, after Reese et al. (1974).Ultimate soil resistan eThe total ultimate lateral resistan e, Fpt,is equal to the passive for e, Fp, minusthe a tive for e, Fa, a ting on the pile.The ultimate resistan e an be estimatedanalyti ally by means of either stati allyor kinemati ally admissible failure modes.At shallow depths a wedge will form infront of the pile assuming that the Mohr-Coulomb failure riterion is valid. Reeseet al. (1974) uses the wedge shown in �g.9 to analyti ally al ulate the passive ulti-mate resistan e at shallow depths, pcs. Byusing this failure mode a smooth pile is as-sumed, and therefore no tangential for eso ur at the pile surfa e. The a tive for eis also omputed from Rankine's failuremode, using the minimum oe� ient of a -tive earth pressure.At deep depths the sand will, in ontrastto shallow depths, �ow around the pile anda stati al failure mode as sket hed in �g.10 is used to al ulate the ultimate resis-tan e. The transition depth between thesefailure modes o urs, at the depth wherethe ultimate resistan es al ulated basedon the two failure modes are identi al.The ultimate resistan e per unit length ofthe pile an for the two failure modes be

14Fp

D

h

Direction of

movement

x

Figure 9: Failure mode at shallow depths, afterReese et al. (1974).Pile

Pile movementShear failure surfaceMovement of blockFigure 10: Failure mode at deep depths, afterReese et al. (1974). al ulated a ording to (12) and (13):

pcs = γ′xK0x tanϕtr sin β

tan(β − ϕtr) cosα(12)

+ γ′xtan β

tan(β − ϕtr)(D − x tan β tanα)

+ γ′x(K0x tanϕtr(tanϕtr sinβ − tanα)

−KaD)

pcd = KaDγ′x(tan8 β − 1) (13)+K0Dγ′x tanϕtr tan

4 β

pcs is valid at shallow depths and pcd atdeep depths, γ′ is the e�e tive unit weight,and ϕtr is the angle of internal fri tionbased on triaxial tests. The fa tors α andβ measured in degrees an be estimated bythe following relations:

α =ϕtr

2(14)

β =45◦ +ϕtr

2(15)Hen e, the angle β is estimated a ordingto Rankine's theory whi h is valid if the

pile surfa e is assumed smooth. The fa torα depends on the fri tion angle and loadtype. However, the e�e t of load type isnegle ted in (14). Ka and K0 are the oef-� ients of a tive horizontal earth pressureand horizontal earth pressure at rest, re-spe tively:

Ka = tan2(45 −ϕtr

2) (16)

K0 = 0.4 (17)The value of K0 depends on several fa -tors, e.g. the fri tion angle, but (17) doesnot re�e t that.The theoreti al ultimate resistan e, pc, asfun tion of depth is shown in �g. 11.As shown, the transition depth in reaseswith diameter and angle of internal fri -tion. Hen e, for piles with a low slender-ness ratio the transition depth might ap-pear far beneath the pile-toe.By omparing the theoreti al ultimate re-sistan e, pc, with the full-s ale tests atMustang Island, Cox et al. (1974) founda poor agreement. Therefore, a oe� ientA is introdu ed when al ulating the a -tual ultimate soil resistan e, pu, employedin the p�y urve formulations:

pu = Apc (18)The variation of the oe� ient A withnon-dimensional depth, x/D, depends onwhether stati or y li loading is applied.The variation of A is shown in �g. 12a.The deformation ausing the ultimate soilresistan e, yu, f. �g. 8, is de�ned as3D/80.p�y urve formulationThe soil resistan e per unit length, pm, atym = D/60, f. �g. 8, an be al ulatedas:

pm = Bpc (19)B is a oe� ient depending on the non-dimensional depth x/D, and whether sta-ti og y li loading is onsidered. The va-riation of B with non-dimensional depth is

15

0 1 2 3 4 5 6

x 104

0

5

10

15

20

25

30

pc [kN/m]

x [m

]

φtr=30°

φtr=40°

(a) D = 1.0 m0 1 2 3 4 5 6

x 105

0

20

40

60

80

100

120

pc [kN/m]

x [m

]

φtr=30°

φtr=40°

(b) D = 4.0 mFigure 11: Theoreti al ultimate resistan e, pc,as fun tion of the depth. γ′= 10 kN/m3 has beenused to plot the �gure. The transition depths aremarked with ir les.illustrated in �g. 12b. Hen e, y li load-ing is taken into a ount by a redu tion ofthe non-dimensional onstants A and B.Cy li loading only a�e ts the p�y urvessigni� antly at depths from the soil surfa eto x/D = 3.5.The slope of the initial straight line, p1as shown in �g. 8, depends on the initialmodulus of subgrade rea tion, k, and thedepth x. This is due to the fa t that the in-situ Young's modulus of elasti ity also in- reases with depth. Further, it is assumedthat the slope of the initial straight linein reases linearly with depth sin e labora-tory test shows, that the initial slope of thestress-strain urve for sand is a linear fun -tion of the on�ning pressure, f. Terzaghi(1955). The initial tangent sti�ness of the

(a) Non-dimensional oe� ient A for de-termining the ultimate soil resistan e, pu.

(b) Non-dimensional oe� ient B for de-termining the soil resistan e, pm.Figure 12: Non-dimensional variation of A andB, after Reese et al. (1974).p�y urves is in the following denoted E∗

py.The initial straight line is given by:p1(y) = E∗

pyy = kxy (20)Reese et al. (1974) suggest that the valueof k only depends on the relative den-sity/internal fri tion angle for the sand.On basis of full-s ale experiments values ofk for loose sands, for medium dense sands,and for dense sands are 5.4 MN/m3 (20lbs/in3), 16.3 MN/m3 (60 lbs/in3), and 34MN/m3 (125 lbs/in3), respe tively. Thevalues are valid for sands below the wa-ter table. Earlier estimations of k hasalso been made, for example by Terza-ghi (1955), but a ording to Reese andVan Impe (2001) these methods have been

16based on intuition and insight. Design reg-ulations, e.g. API (2000) and DNV (2010),re ommend the use of the urve shown in�g. 13. The urve only shows data forrelative densities up to approximately 80%, whi h auses large un ertainties in theestimation of k for very dense sands.

Relative density [%]

Below thewater table

Above thewater table

V. Loose

28

0 20 40 60 80 100

80000

70000

60000

50000

40000

30000

20000

10000

0

29 30 36 40 45

Loose Medium dense Dense V. dense

Friction angle, [degrees]

k[kPa

/m]

Figure 13: Variation of initial modulus of sub-grade rea tion k as fun tion of relative density,after API (2000).The equation for the parabola, p2, f. �g.8, is des ribed by:p2(y) = Cy1/n (21)where C and n are onstants. The onstants and the parabola's start point(yk,pk) are determined by the following riteria:p1(yk) = p2(yk) (22)p2(ym) = p3(ym) (23)

∂p2(ym)

∂y=

∂p3(ym)

∂y(24)The onstants an then be al ulated by:

n =pmmym

(25)C =

pm

y1/nm

(26)yk = (

C

kx)n/(n−1) (27)where m is the slope of the line, p3.

3.3 Method BO'Neill and Mur hison suggested a mod-i�ed formulation of the p�y urves. Themodi�ed expression is urrently re om-mended in the design regulations, e.g. API(2000) and DNV (2010). In their modi�edp�y urve formulation, the analyti al ex-pressions for the ultimate soil resistan e,(12) and (13), are approximated using thedimensionless parameters C1, C2 and C3:

pu = min

(

pus = (C1x+C2D)σ′

v

pud = C3Dσ′

v

)(28)The onstants C1, C2 and C3 an be de-termined from �g. 14.25 30 35 40 450

1

2

3

4

5

6

friction angle, φ [degrees]

C1 a

nd C

2 [−]

2C1C

(a) C1 and C2.25 30 35 40 450

20

40

60

80

100

120

friction angle, φ [degrees]

C3 [−

]

3C

(b) C3.Figure 14: Variation of the parameters C1, C2and C3 as fun tion of angle of internal fri tion,after API (2000).A hyperboli formula is used to des ribethe relationship between soil resistan eand pile de�e tion instead of a pie ewiseformulation as proposed by method A:p(y) = Apu tanh

(

kx

Apuy

) (29)

17The oe� ient A ould either be deter-mined from �g. 12a or by:A =

(

3.0− 0.8HD ≥ 0.9 , stati loading

0.9 , y li loading )(30)Sin e:dp

dy|y=0= Apu

kxApu osh2( kxyApu

)|y=0= kx (31)the p�y urve's initial slope is then similarusing the two methods, f. (20). Also theupper bound of soil resistan e will approx-imately be the same. However, there isa onsiderable di�eren e in soil resistan epredi ted by the two methods when on-sidering the pile de�e tion between yk and

yu as shown in �g. 15. The soil parametersfrom tab. 1 has been used to onstru t thep�y urves shown in �g. 15.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

500

1000

1500

2000

2500

3000

y [m]

p [k

N/m

]

Method AMethod Bkmu

x = 10 m

x = 5 m

Figure 15: Example of p�y urves based onmethod A and B. The points k, m, and u refers tothe points (yk,pk), (ym,pm), and (yu,pu), respe -tively, f. �g. 8.Table 1: Soil parameters used for plotting thep�y urves in �g. 15.

γ′ φtr D k[kN/m3℄ [◦℄ [m℄ [kN/m3℄10 30 4.2 80003.4 Comparison of methodsA omparison of both stati and y li p�y urves has been made by Mur hison and

O'Neill (1984) based on a database of 14full-s ale tests on 10 di�erent sites. Thepile diameters varied from 51 mm (2 in.)to 1.22 m (48 in.). Both timber, on reteand steel piles were onsidered. The soilfri tion angles ranged from 23◦ to 42◦. Thetest piles' slenderness ratio's are not pro-vided.Mur hison and O'Neill (1984) omparedthe p�y urve formulations formulated byReese et al. (1974), Bogard and Mat-lo k (1980), S ott (1980), and O'Neill andMur hison (1983) with the full-s ale testsusing the Winkler approa h. The pre-di ted pile-head de�e tion, maximum mo-ment, Mmax, and the depth of maximummoment were ompared a ording to theerror, E:E =

|predi ted value - measured value|measured value (32)In the analysis it was desired to assessthe formulations ability to predi t the be-haviour of steel pipe monopiles. Multi-pli ation fa tors were therefore employed.The error, E, was multiplied by a fa tor oftwo for pipe piles, 1.5 for non-pipe drivenpiles and a fa tor of one for drilled piers.When predi ted values were lower than themeasured values the error was multipliedby a fa tor of two. By using these fa -tors un onservative results are penalisedand pipe piles are valued higher in the omparison. In tab. 2 the average valueof E for stati p�y urves are shown forthe four methods, and in tab. 3 the aver-age value of E is shown for the y li p�y urves. As shown, the formulation pro-posed by O'Neill and Mur hison (1983), f. method B, results in a lower averagevalue of E. The standard deviation of Ewas not provided in the omparison.In their omparison of the four p-y urveformulations with the database of tests,Mur hison and O'Neill (1984) observedthat method A often predi ted largerdispla ement than what was measured.Hen e, method A seems to be onserva-

18Table 2: Average values of the error, E, for the sta-ti pile tests. The methods are ompared for pile-headde�e tion, maximum moment and depth to maximummoment. Pile-head Mmax Depth tode�e tion MmaxReese etal. (1974) 2.08 0.75 0.58Bogard andMatlo k(1980) 1.95 0.73 0.52S ott (1980) 2.31 0.58 0.37O'Neill andMur hison(1983) 1.44 0.44 0.40Table 3: Average values of the error, E, for the y li pile tests. The methods are ompared for pile-head de-�e tion, maximum moment and depth to maximum mo-ment. Pile-head Mmax Depth tode�e tion MmaxReese etal. (1974) 1.15 0.61 0.16Bogard andMatlo k(1980) 1.22 0.55 0.12O'Neill andMur hison(1983) 0.55 0.5 0.16tive. In ontrast method B were neitherfound to be onservative nor un onserva-tive.Mur hison and O'Neill (1984) analysedthe sensitivity to parameter variation formethod B. The initial modulus of sub-grade rea tion, k, the internal fri tion an-gle, ϕ, and the e�e tive unit weight, γ′,were varied. They found that a 10 % in- rease in either ϕ or γ′ resulted in an in- rease in pile-head de�e tion of up to 15and 10 %, respe tively. For an in rease of25 % in k an in rease of up to 10 % of thepile-head de�e tion was found. The sen-sitivity analysis also shows that k has thegreatest in�uen e on pile-head de�e tionat small de�e tions and that ϕ has a great

in�uen e at large de�e tions. Mur hisonand O'Neill (1984) state that the sizes ofthe errors in tab. 2 annot be explainedby parameter un ertainties. The amountof data in luded in the database was verysmall due to the unavailability of appro-priately do umented full-s ale tests andMur hison and O'Neill (1984) therefore on luded that a further study of the soil-pile intera tion was needed.4 Limitations of p�y urvesThe p�y urve formulations for piles in o-hesionless soils are developed for piles withdiameters mu h less than 4 to 6 m whi his often ne essary for nowadays monopiles.Today, there is no approved method fordealing with these large-diameter, non-slender o�shore piles, whi h is why the de-sign regulations are still adopting the orig-inal p�y urve formulations (Reese et al.,1974; O'Neill and Mur hison, 1983; API,2000; and DNV, 2010).The p�y urve formulations are derived onthe basis of the Mustang Island tests whi hin luded only two identi al piles and a to-tal of seven load ases. Furthermore, thetests were ondu ted for only one pile dia-meter, one type of sand, only ir ular pipepiles, et . Taking into a ount the numberof fa tors that might a�e t the behaviourof a laterally loaded pile and the very lim-ited number of full-s ale tests performedto validate the method, the in�uen e ofa broad spe tra of parameters in the p�y urves are still to be lari�ed. When onsidering o�shore wind turbine founda-tions a validation of sti� piles with a slen-derness ratio of L/D < 10 is needed. Itis desirable to investigate this as it mighthave a signi� ant e�e t on the initial sti�-ness whi h is not a ounted for in the p�y urve method. Briaud et al. (1984) postu-late that the soil response depends on the�exibility of the pile. Criteria for sti� ver-sus �exible behaviour of piles have been

19proposed by various authors, for example,Dobry et al. (1982), Budhu and Davies(1987), and Poulus and Hull (1989). Thedi�eren e in deformation behaviour of asti� and a �exible pile is shown in �g.16. A pile behaves rigidly when the follow-ing riterion is full�lled (Poulus and Hull,1989):L < 1.48

(

EpIpEs

)0.25 (33)Es is Young's modulus of elasti ity of thesoil. The riterion for �exible pile be-haviour is (Poulus and Hull, 1989):

L > 4.44

(

EpIpEs

)0.25 (34)A ording to (33) a monopile with anouter diameter of 4 m, an embedded lengthof 20 m and a wall thi kness of 0.05 m be-haves rigidly if Es < 7.6 MPa. In on-trast, the pile exhibits a �exible behaviourif Es > 617 MPa. Even dense sands haveEs < 100 MPa, so the re ently installedmonopiles for o�shore wind turbines be-have, more like rigid than �exible piles.

Figure 16: Rigid versus �exible pile behaviour.The urrent expression for the ultimatesoil resistan e is an analyti al expressionderived for a lateral pile translation. A orre tion fa tor for the ultimate soil resis-tan e based on full-s ale tests on �exiblepiles is emloyed. However, as monopilesfor o�shore wind turbines behave morerigidly than �exibly the ombination of theanalyti al expression and the orre tionfa tor might be a poor approximation of

the ultimate soil resistan e for rigid piles.Hen e, the ultimate soil resistan e needsvalidation for large-diameter, non-slenderpiles.Only small pile-head rotations are a ept-able for modern wind turbine foundations.The allowable pile rotation is provided bythe wind turbine supplier. Typi ally 0.5◦of a umulated plasti pile rotation is a - eptable. Furthermore, it is of high im-portan e to avoid resonan e of the windturbine with the blade frequen y, the rotorfrequen y and the energy ri h frequen y ofthe loading. Hen e, it is important to mo-del the foundation sti�ness orre tly. Ap-propriate values for the initial sti�ness ofthe p�y urves are therefore ne essary.When using the p�y urve method, the pilebending sti�ness is employed when solvingthe beam on an elasti foundation prob-lem. However, no importan e is given tothe pile bending sti�ness in the formula-tion of the p�y urves. Hen e, Epy is inde-pendent of the pile properties. The valid-ity of this assumption an be questioned asEpy is a parameter des ribing the soil-pileintera tion.When de oupling the non-linear springsasso iated with the Winkler model ap-proa h another error is introdu ed, sin ethe soil in reality a ts as a ontinuum.The design regulations suggests the use ofa tangent hyperboli p�y urve, f. (29).The reason for this is based on the ompar-ison reported by Mur hison and O'Neill(1984) of four di�erent p�y urve formu-lations. When using this approa h, theinitial slope of the p�y urves and the ul-timate soil resistan e governs the shapeof the urve. However, the validity ofthe tangent hyperboli formulation an bequestioned.The p�y urve formulation is based on full-s ale tests on piles installed in rather ho-mogeneous soil. However, often piles areto be installed in a strongly layered strat-

20i� ation. The e�e t of layered soil on thesoil-pile intera tion therefore needs to beinvestigated.O�shore wind turbines are exposed to y li loading from wind and waves. Dur-ing the lifetime of an o�shore wind turbine(typi ally 20 years) the foundation will beexposed to few load y les of high load am-plitude and 106 − 108 load y les of lowto intermediate load amplitude. The p�y urve formulations proposed by Reeseet al. (1974) and O'Neill and Mur hison(1983) are based on full-s ale tests on pilesfor the oil and gas se tor. In these full-s ale tests, the pile behaviour for y li loading with up to 100 load y les was in-vestigated. Hen e, the behaviour of thepiles with respe t to long-term y li load-ing were not investigated. The a umu-lated pile de�e tion and the hange in pilesti�ness due to long-term y li loadingtherefore needs to be adressed.Around pile foundations in the o�shore en-vironment, erosion of soil material an o - ur due to turbulen e. S our holes willtherefore form around the pile founda-tions. S our is espe ially an issue for o-hesionless soil materials. S our holes anwhen they are fully developed be up to1.3D (DNV, 2010). When a s our hole hasbeen formed, soil support is lost. Hen e,the p�y urves needs modi� ation to a - ount for s our.In the following a number of assumptionsand not lari�ed parameters related to thep�y urve method are treated separately.The treated assumptions and parametersare:� Shearing for e between soil layers.� The ultimate soil resistan e.� The in�uen e of verti al pile load onlateral soil response.� E�e t of soil-pile intera tion.

� E�e t of diameter on initial sti�nessof p�y urves.� Choi e of horizontal earth pressure oe� ient.� Shearing for e at the pile-toe.� Shape of p�y urves.� Layered soil.� Long-term y li loading.� S our e�e t on the soil-pile intera -tion.4.1 Shearing for e between soillayersEmploying the Winkler model approa h,the soil response is divided into layers ea hrepresented by non-linear springs. As thesprings are un oupled, the layers are on-sidered to be independent of the lateralpile de�e tion above and below that spe- i� layer, giving that the soil layers are onsidered as smooth layers able to moverelatively to ea h other without loss of en-ergy to fri tion. Pasternak (1954) modi-�ed the Winkler approa h by taking theshear stress between soil layers into a - ount. The soil resistan e per length ofthe pile is given by:p(y) = −Ep

pyy −Gsdy

dx(35)where Gs is the soil shear modulus. Thetraditional subgrade rea tion modulus,

Epy = p/y, may indire tly ontain the soilshear sti�ness as the p�y urve formula-tion has been �tted to full-s ale tests. Eppy, f. (35), is a modulus of subgrade rea tionwithout ontribution from the soil shearsti�ness.Belkhir et al. (1999) examines the signi�- an e of shear between soil layers by om-paring the CAPELA design ode, whi h an take the shear between soil layers intoa ount, with the Fren h PILATE design

21 ode, whi h employes smooth boundaries.The two design odes are ompared withthe results of 59 entrifuge tests ondu tedon long and �exible piles. Analyses show on ordan e between the two design odeswhen shear between soil layers is not takeninto a ount. Furthermore, the analysesshows a redu tion varying from 5 % to14 % in the di�eren e between the max-imum moments determined from the en-trifuge tests and the numeri al simulationswhen taking the shear between the soil lay-ers into a ount. However, it is not learfrom the paper whether or not the shearbetween soil layers is dependent on pileproperties su h as pile diameter, slender-ness ratio, et . Furthermore, it is not lar-i�ed whether the authors distinguish be-tween Epy and Eppy.4.2 The ultimate soil resistan eThe p�y urve formulations a ording toMethod A and Method B are both depen-dent on the ultimate soil resistan e. Themethod for estimation of pu is thereforeevaluated in the following.Failure modesWhen designing large-diameter monopilesin sand, the transition between the pre-sumed failure modes will most often o urbeneath the pile-toe, f. �g. 11b. There-fore, the ultimate soil resistan e at shal-low depths is governing for monopile foun-dations for o�shore wind turbines. How-ever, several un ertainties on erning theexpression for the ultimate soil resistan eat shallow depths exist.The pres ribed method for al ulating theultimate soil resistan e at shallow depthsassumes that the pile is smooth, whi hmeans that no skin fri tion appears be-tween the pile wall and the soil, and fur-ther the formation of a Rankine failureis assumed. However, in reality a pile

is neither perfe tly rough nor perfe tlysmooth, and the assumed failure me ha-nism is therefore not orre t. A ordingto Harremoës et al. (1984) a Rankine fail-ure takes pla e for a perfe tly smooth walland a Prandtl failure for a perfe tly roughwall. Sket hes of the two types of failureare shown in �g. 17a and �g. 17b, re-spe tively. Due to the fa t that the pile isneither smooth nor rough a ombination ofa Rankine and Prandtl failure will o ur.(a) Failure mode proposed by Rankine fora smooth interfa e at shallow depth.(b) Failure mode proposed by Prandtl for a roughinterfa e at shallow depth.Figure 17: Rankine and Prandtl failure modes.In (12) the angle α, whi h determines thehorizontal spread of the wedge, appears.Through experiments Reese et al. (1974)postulate that α depends on both the voidratio, the fri tion angle, and the type ofloading. However, the in�uen e of void ra-tio and type of loading is negle ted in theexpression of α, f. (14).Monopiles for o�shore wind turbines arenon-slender piles with high bending sti�-ness. The piles therefore de�e t as almostrigid piles. As the piles are exposed to e - entri loading, the pile deformation pat-tern primarily onsists of rotation around

22a point of zero de�e tion. Hen e, the pilede�e tion at the pile toe is negative. How-ever, when al ulating the ultimate soil re-sistan e a ording to method A and B therotational pile behaviour and hereby ne-gative pile de�e tions beneath the pointof zero de�e tion is disregarded. For non-slender piles, a failure mode as shown in�g. 18 ould potentially form. This fail-ure mode is derived for a two-dimensional ase assuming a smooth pile surfa e. Thefailure mode onsists of sti� elasti zonesand Rankine failures.Figure 18: Possible failure mode for a non-slender pile at shallow depth, after Harremoës etal. (1984).Soil dilatan yThe e�e t of soil dilatan y is not in ludedin method A and B, and thereby the e�e tsof volume hanges during pile de�e tionare ignored.Fan and Long (2005) investigated thein�uen e of soil dilatan y on the ulti-mate soil resistan e by use of a three-dimensional, non-linear �nite element mo-del. The onstitutive model proposed byDesai et al. (1991) in orporating a non-asso iative �ow rule was employed in theanalyses. The �nite element model was alibrated based on the full-s ale tests atMustang Island. The magnitudes of ul-timate soil resistan e were al ulated fortwo ompa tions of one sandtype withsimilar fri tion angles (ϕtr = 45◦) but dif-ferent angles of dilatan y. The dilatan yangles are not dire tly spe i�ed by Fanand Long (2005). Estimates have therefore

been made by interpretation of the rela-tion between volumetri strains and axialstrains. Dilatan y angles of approximately22◦ and 29◦ were found. An in rease inultimate soil resistan e of approximately50 % were found with the in rease in dila-tan y angle. In agreement with laboratorytests, where the dilatan y in dense sands ontributes to strength, this makes goodsense. It should be noted that the dila-tan y angle and the soil fri tion angle arerelated su h that soil materials with a highvalue for the fri tion angle typi ally alsohas a high value for the dilatan y angle.Hen e, the e�e t of soil dilatan e might beimpli itly in orporated in the expressionfor the ultimate resistan e and the orre -tion fa tor A. Further, it should be notedthat a urate determination of the dila-tan y angles requires expensive soil tests,for example, triaxial tests.Alternative methodsBesides the pres ribed method for al u-lating the ultimate soil resistan e severalother formulations exist (e.g. Hansen,1961; Broms, 1964; Petrasovits andAward, 1972; Meyerhof et al., 1981; andPrasad and Chari, 1999). Fan and Long(2005) ompared the methods of Hansen(1961) and Broms (1964) with method Band a �nite element solution. In the om-parison, the pile diameter, the fri tion an-gle, and the oe� ient of horizontal earthpressure were varied. Hansen's methodshowed the best orrelation with the �niteelement model, whereas Broms' methodresulted in onservative values of the ulti-mate soil resistan e. Further, a signi� antdi�eren e between the �nite element solu-tion and method B was found. Method Bwas found to produ e onservative resultsat shallow depths and non- onservative re-sults at deep depths. The results of the omparison are shown in �g. 19.The expression of the ultimate soil re-sistan e formulated by Hansen (1961),

23

Figure 19: Comparison of the ultimate soil resistan e estimated by Broms' method, Hansen's method,and method B with a �nite element model, after Fan and Long (2005). pult/pult(fem) de�nes the ratioof the ultimate soil resistan e al ulated by the analyti al methods and the ultimate soil resistan e al ulated by the �nite element model.Broms (1964), Petrasovits and Award(1972), Meyerhof et al. (1981), and Reeseet al. (1974) all assumes the soil pres-sure to vary uniformly with the pile width.Prasad and Chari (1999) formulated an ex-pression based on small-s ale tests on rigidpiles instrumented with pressure transdu -ers. They measured the variation of soilpressure with depth and horizontal posi-tion on the pile. The test piles had di-ameters of 0.102 m and slenderness ra-tios of 3-6. They determined failure asthe point in whi h the load-displa ement urves started to be linear. Hen e, a hor-

izontal asymptote was not rea hed and it an be argued whether or not their de�-nition of failure is reasonable. Various re-sear hers have expressed riteria for pilefailure, for instan e, LeBlan et al. (2010).They onsidered a horizontally loaded pileto be in failure when the normalised pilerotation, Θ, ex eeds 4 ◦. They de�ned thenormalised pile rotation as:Θ = Θ

√

paγ′L

(36)Failure was by Prasad and Chari (1999)found at pile displa ements of 0.2-0.4D.

24Based on the load tests on rigid piles, theyformulated a new expression for the ul-timate soil resistan e for laterally loadedrigid piles in whi h the ultimate soil re-sistan e depends on parameters su h asthe fri tion angle, the pile diameter, thepile length and the depth of the pointof zero pile de�e tion. Their expression onsists of three linear urves des ribingthe variation of the ultimate soil resis-tan e with depth. The expressions ofHansen (1961), Broms (1964), Petrasovitsand Award (1972), Meyerhof et al. (1981)and Prasad and Chari (1999) are sket hedin �g. 20. All ex ept Prasad and Chari(1999) postulate that the ultimate resis-tan e at the depth of zero pile de�e tionis non-zero.When al ulating the ultimate soil resis-tan e a ording to method A and B, theside fri tion as illustrated in �g. 21 is ne-gle ted. To take this into a ount Briaudand Smith (1984) has proposed a modelwhere the ultimate soil resistan e, pu, is al ulated as the sum of the net ultimatefrontal resistan e, Q, and the net ultimateside fri tion, F :pu = Q+ F = (ηPmax + ξτmax)D (37)

Figure 21: Side fri tion and soil pressure on thefront and the ba k of the pile due to lateral de-�e tion.where Pmax denotes the maximum frontalsoil pressure a ting on the pile, τmax de-notes the maximum shear stress a ting onthe pile, and η and ξ are dimensionless onstants. For ir ular piles Zhang et al.

(2005) re ommends the use of (38)-(41) forPmax, τmax, η and ξ.

Pmax = K2pγx (38)

τmax = Kγx tan(δ) (39)η = 0.8 (40)ξ = 1.0 (41)Zhang et al. (2005) propose the side fri -tion and frontal resistan e to vary withdepth similar to the variation proposed byPrasad and Chari (1999). They omparedtheir method with small- and large-s aletests and found their method to be slightly onservative as the pile apa ities al u-lated by their proposed method in aver-age was 8 % smaller than the meassuredpile apa ities. Further, parameters su has the embedded pile length, the slender-ness ratio, the e entri ity ratio, e/L, andthe fri tion angle did not a�e t the a u-ra y of their method, f. �g. 22.The importan e of in luding side fri tionin the formulation of p�y urves is for themodel proposed by Zhang et al. (2005)una�e ted by the diameter sin e both theultimate frontal resistan e and the net ul-timate side fri tion vary linearly with dia-meter. However, the ultimate frontal re-sistan e varies non-linearly with diame-ter in the model proposed by Reese etal. (1974). The importan e of side fri -tion might therefore be more signi� ant forlarge-diameter monopiles than for small-diameter piles.SummarySeveral assumptions are employed when al ulating the ultimate soil resistan e a - ording to Reese et al. (1974) and the de-sign regulations, e.g. API (2000) and DNV(2010). These methods do not a ountfor fri tion between pile and soil as thepile surfa e is assumed smooth. Further-more, the failure modes are determined

25

Figure 20: Sket h of the expressions of ultimate resistan e proposed by Hansen et al. (1961), Broms(1964), Petrasovits and Award (1972), Meyerhof et al. (1981) and Prasad and Chari (1999), Zhang etal. (2005).0 1 2 3 4 5 6

−40

−20

0

20

40

60

Pile length, L [m]

Err

or [%

]

4 6 8 10 12 14 16−40

−20

0

20

40

60

Slenderness ratio, L/D [−]

Err

or [%

]

0 1 2 3 4−40

−20

0

20

40

60

Eccentricity ratio, e/L [−]

Err

or [%

]

30 35 40 45 50−40

−20

0

20

40

60

Friction angle, φ [°]

Err

or [%

]

Figure 22: Error in per ent between between the predi ted pile apa ity estimated by means of themethod by Zhang et al. (2005) and experimental tests, after Zhang et al. (2005)for lateral pile translation. Hen e, de�e -tions beneath the point of zero pile de�e -tion are a ounted for in a very simpli�edmaner. Thus, the assumed failure modesare ina urate espe ially for non-slenderpiles.The dilatan y of the soil a�e ts the soilstrenght, but it is negle ted in the expres-sions for the ultimate soil resistan e.Several methods for determining the ul-timate soil resistan e exist. The methodproposed by Hansen (1961) were found to

26 orrelate better with a �nite element mo-del than the methods proposed by Reeseet al. (1974) and Broms (1964). In orderto take the e�e t of side fri tion into a - ount a model was proposed by Zhang etal. (2005) based on the �ndings of Briaudand Smith (1984) and Prasad and Chari(1999). Predi tions regarding the ultimatesoil resistan e orrelate well with labora-tory and full-s ale tests when using thismodel.4.3 The in�uen e of verti al loadon lateral soil responseIn urrent pra ti e, piles are anal-ysed separately for verti al and hor-izontal behaviour. Karthigeyan etal. (2006), Abdel-Rahman and A hmus(2006), A hmus et al. (2009a), andA hmus and Thieken (2010) investigatedthe e�e t of ombined stati verti aland lateral loading on the lateral andverti al pile response in sand throughthree-dimensional numeri al modelling.Karthigeyan et al. (2006) adopted aDru ker-Prager onstitutive model with anon-asso iated �ow rule in their numeri almodelling. Abdel-Rahman and A hmus(2006), A hmus et al. (2009a) and A hmusand Thieken (2010) all adopted the Mohr-Coulomb onstitutive model with a non-asso iated �ow rule. Further, they mod-elled the soil sti�ness as stress-dependent.Karthigeyan et al. (2006) alibratedthe numeri al model against two di�erentkinds of �eld data arried out by Kara-sev et al. (1977) and Comodromos (2003).A on rete pile with a diameter of 0.6 mand a slenderness ratio of 5 were tested, f. Karasev et al. (1977). The soil strata onsisted of sti� sandy loam in the top6 m underlain by sandy lay. Comodro-mos (2003) performed the tests in Gree e.The soil pro�le onsisted of silty lay nearthe surfa e with thin sublayers of loosesand. Beneath a medium sti� lay layera very dense sandy gravel layer was en-

ountered. A pile with a diameter of 1 mand a slenderness ratio of 52 were tested.A reasonable agreement between the �eldtests and the numeri al model was found.A hmus and Thieken (2010) validatedtheir numeri al model against the modeltests of Das et al. (1976) and Meyer-hof and Sastry (1985). A good agreementwere found. Abdel-Rahman and A hmus(2006) did not report whether their numer-i al model was validated against exper-imental tests. However, Abdel-Rahmanand A hmus (2006) and A hmus andThieken (2010) both used the ommer- ial three-dimensional �nite element pro-gramme ABAQUS and further they em-ployed similar onstitutive models. There-fore, the numeri al model employed byAbdel-Rahman and A hmus (2006) is as-sumed also to �t the stati model testswell.To investigate the in�uen e of verti alload on the lateral response in sand,Karthigeyan et al. (2006) modelled asquared on rete pile (1200 × 1200 mm)with a length of 10 m. Two types of sandwere tested, a loose and a dense sand withfri tion angles of 30◦ and 36◦, respe tively.The verti al load was applied in two dif-ferent ways, simultaneously with the lat-eral load (SAVL) and prior to the lateralload (VPL). Compressional verti al load-ing with values of 0.2, 0.4, 0.6, and 0.8times the verti al pile apa ity were ap-plied. The on lusion of the analyses wasthat the lateral apa ity of piles in sandin reases under verti al loading. The in- rease in lateral apa ity depended on howthe verti al load was applied and on therelative density of the soil. The highestin rease was in the ase of VPL with adense sand. For the dense sand with a lat-eral de�e tion of 5 % of the side lengththe in rease in lateral apa ity was, in the ase of SAVL, of up to 6.8 %. The samesituation in the ase of VPL resulted inan in rease of up to 39.3 %. Due to verti- al loads higher verti al soil stresses andthereby higher horizontal stresses o ur,

27whi h also mobilise larger fri tion for esalong the length of the pile. Therefore, thelateral apa ity in reases under the in�u-en e of verti al loading.Abdel-Rahman and A hmus (2006),A hmus et al. (2009a) and A hmus andThieken (2010) analysed the e�e t of ombined verti al and lateral loading onboth the verti al and lateral pile sti�nessand apa ity. Furthermore, they both onsidered ompressive as well as tensileverti al loading. Abdel-Rahman andA hmus (2006) modelled the behaviour ofhollow steel piles with pile diameters of2.0 and 3.0 m and embedded pile lengthsof 20 m, A hmus et al. (2009a) modelled on rete piles with diameters of 2.0 mand pile lengths of 10 and 30 m, whileA hmus and Thieken (2010) modelled thebehaviour of reinfor ed on rete piles withdiameters of 0.5-3.0 m and embedded pilelengths of 15 m. They all onsidered pilesinstalled in medium dense sand with afri tion angle of 35◦. The verti al and lat-eral loading was applied simultaneously.Abdel-Rahman and A hmus (2006) foundthat for axial ompression the e�e t of ombined loading in reases both the pilelateral sti�ness and pile lateral apa ity,allthough the in rease was very moderate.The verti al sti�ness and apa ity werefound to in rease signi� antly. The e�e tof ombined loading was found to bemore signi� ant for rigid than �exiblepiles. This on�rms the results reportedby Karthigeyan et al. (2006). For axialtension no hange were found in thelateral pile sti�ness. However, the lateralpile apa ity was found to de rease for ombined loading. The verti al pilesti�ness was found to de rease, while theverti al apa ity was found to in reasefor ombined lateral and verti al loading.The numeri al modelling of A hmus etal. (2009a), and A hmus and Thieken(2010) on�rmed the observations ofAbdel-Rahman and A hmus (2006).Furthermore they presented intera tiondiagrams to be used for ombined loading.

The above mentioned analysis of the ef-fe t of ombined lateral and verti al load-ing on the lateral pile behaviour empha-size that both the verti al sti�ness and a-pa ity as well as the lateral sti�ness and apa ity are positively a�e ted when theverti al loading is ompressive. However,the e�e t is small when the verti al andlateral loads are applied simultaneously.Foundations for o�shore wind turbines areexhibited to a onstant verti al ompres-sive load originating from the selfweight ofthe turbine and the foundation itself. In ontrast, the horizontal loading is y li .Hen e, the verti al loading is applied priorto the lateral loading, and ombined load-ing might therefore signi� antly in reasethe pile sti�ness and apa ity of monopilesfor o�shore wind turbines. However, itshould be emphasized that ombined load-ing needs to be examined for y li load-ing and that the above mentioned �ndingsneeds to be examined further through ex-perimental testing.4.4 E�e t of soil-pile intera tionNo importan e is atta hed to the pilebending sti�ness, EpIp, in the formula-tion of the p�y urves. Hereby, Epy isindependent of the pile properties, whi hseems questionable as Epy is a soil-pile in-tera tion parameter. Another approa hto predi t the response of a �exible pileunder lateral loading is the strain wedge(SW) model developed by Norris (1986).The method in orporates the pile prop-erties. The on ept of the SW mo-del is that the traditional parametersin the one-dimensional Winkler approa h an be hara terised in terms of three-dimensional soil-pile intera tion. The SWmodel was initially established to ana-lyse free-headed piles embedded in uni-form soils. Sin e then it has been im-proved su h that it, for instan e, an a - ount for �xed pile head onditions, lay-ered soils, soil liquefa tion, pile group ef-

28fe ts, and y li loading (Ashour et al.,1998; Ashour and Norris, 2000; Ashour etal., 2002; Ashour and Norris, 2003; andLesny and Hinz, 2009).The SW model parameters are related to athree-dimensional passive wedge develop-ing in front of the pile subje ted to lateralloading. The wedge has a form similar tothe wedge asso iated with method A, asshown in �g. 9. However the angles α andβ are given by:

α = ϕm (42)β = 45◦ +

ϕm

2(43)where ϕm is the angle of mobilised internalfri tion.The purpose of the method is to relatethe stresses and strains of the soil in thewedge to the subgrade rea tion modulus,

Epy. The SW model des ribed by Ashouret al. (1998) assumes a linear de�e tionpattern of the pile over the passive wedgedepth, h, as shown in �g. 23. The dimen-sion of the passive wedge depends on twotypes of stability: lo al and global stabil-ity. To obtain lo al stability the SWmodelshould satisfy equilibrium and ompatibil-ity between the pile de�e tion, the strainsin the soil and the soil resistan e a ting onthe pile wall. This is obtained by an itera-tive pro edure where an initial horizontalstrain in the wedge is assumed.After assuming a passive wedge depth thesubgrade rea tion modulus an be al u-lated along the pile. Based on the al u-lated subgrade rea tion modulus the pile-head de�e tion an be al ulated fromthe one-dimensional Winkler approa h.Global stability is obtained when on or-dan e between the pile-head de�e tion al- ulated by the Winkler approa h and theSW-model is a hieved. The passive wedgedepth is varied until global stability is ob-tained.The pile bending sti�ness in�uen e thepile de�e tion pattern al ulated by the

Figure 23: Linear de�e tion assumed in the SW-model, shown by the solid line. The dashed lineshows the real de�e tion of a �exible pile. AfterAshour et al. (1998).one-dimensional Winkler approa h andhereby also the wedge depth. Hen e, thepile bending sti�ness in�uen es the p�y urves al ulated by the SW-model.The equations asso iated with the SW mo-del are based on the results of isotropi drained triaxial tests. Hereby an isotropi soil behaviour is assumed at the site. TheSW model takes the real stresses into a - ount by dealing with a stress level, de-�ned as:SL =

∆σh∆σhf

(44)where ∆σh and ∆σhf are the mobilisedhorizontal stress hange and the horizontalstress hange at failure, respe tively. Thespread of the wedge is de�ned by the mo-bilised fri tion angle, f. (42) and (43).Hen e the dimensions of the wedge de-pends on the mobilised fri tion.Although the SW model is based onthe three-dimensional soil-pile intera tion,and although it is dependent on both soiland pile properties, there are still signif-i ant un ertainties related to the model.The model does not take the a tive soilpressure that o urs at the ba k of the pileinto a ount, whi h is a non- onservative onsideration. Furthermore, the wedgeonly a ounts for the passive soil pressureat the top front of the pile and negle tsthe passive soil pressure beneath the zero

29 rossing point whi h will o ur for a non-slender pile, f. se tion 4.2. The assump-tion of an isotropi behaviour of the soil inthe wedge seems unrealisti in most asesfor sand. To obtain isotropi behaviourthe oe� ient of horizontal earth pressure,K, needs to be 1, whi h is not the ase formost sands.Ashour et al. (2002) riti ise the p�y urvemethod as it is based and veri�ed througha small number of tests. However, theSW model, has a ording to Lesny et al.(2007) been veri�ed only for slender piles.Ashour and Norris (2000) investigated bymeans of the SW model, the in�uen e ofpile sti�ness on the lateral response for onditions similar to the Mustang Islandtests. p�y urves at a depth of 1.83 mare shown in �g. 24 for di�erent values ofEpIp. The p�y urve proposed by Reeseet al. (1974) is also presented in the �g-ure. It is seen that there is a good on or-dan e between the p�y urve formulationproposed by Reese et al. (1974) and theSW model for similar pile properties. Itshould be noted that in �g. 24, the p�y urve determined by means of the SW mo-del depends on the pile bending sti�nesssu h that an in rease in the pile bendingsti�ness results in an in rease in both thesti�ness and the ultimate apa ity of thep�y urves. For other pile and soil proper-ties, Ashour and Norris (2000), found thatan in rease in the pile bending sti�ness ledto less sti� p�y urves. Hen e, they on- lude that the pile bending sti�ness a�e tsthe p�y urves, but that the e�e t is de-pendent on the type of soil and the typeof loading. Furthermore, they found thatthe e�e t of pile bending sti�ness on theSW p�y urves is more signi� ant for densesoils than for loose soils.By means of the SW model Ashour andNorris (2000) found that the pile bendingsti�ness a�e ts the shape of the p�y urvessigni� antly. Fan and Long (2005) inves-tigated the e�e t of pile bending sti�ness

Figure 24: The in�uen e of pile bending sti�-ness, after Ashour et al. (2000).on the soil-pile intera tion for piles situ-ated in sand by means of numeri al mod-elling. Fan and Long (2005) employed the onstitutive model proposed by Desai etal. (1991). Both numeri al models werevalidated against �eld tests. They al u-lated p�y urves by integration of the nor-mal and shear stresses in soil surroundingthe pile. Fan and Long (2005) did not �ndan e�e t of the pile bending sti�ness onthe shape of the p�y urves. In �g. 25p�y urves al ulated by means of the nu-meri al model by Fan and Long an beobserved for varying depht below soil sur-fa e and varying pile bending sti�ness. Forpiles situated in layey soil, Kim and Jeong(2011) found similar results. They also in-vestigated the e�e t of bile bending sti�-ness by means of numeri al modelling.The on lusions of Fan and Long (2005)as well as Kim and Jeong (2011) ontra-di ts the �ndings of Ashour and Norris(2000). More insight into the e�e t of thepile bending sti�ness on the soil-pile inter-a tion is therefore needed.4.5 E�e t of diameter on initialsti�ness of p�y urvesThe initial modulus of subgrade rea -tion, k, is a ording to API (2000), DNV(2010), and Reese et al. (1974) only de-pendent on the relative density of the

30

Figure 25: E�e t of pile bending sti�ness, afterFan and Long (2005).soil. The dependen y is shown in �g. 13.Hen e, the methods A and B do not in- lude EpIp and D in the determination ofk. Di�erent studies on the onsequen es ofnegle ting the pile parameters have been ondu ted over time with ontradi tory on lusions. Ashford and Juirnarongrit(2003) point out the following three on- lusions in a summarization of previous re-sear h:� Terzaghi (1955) analysed the e�e tof pile diameter on the modulus ofsubgrade rea tion by onsideration ofstress bulbs forming in front of later-ally loaded piles. Terzaghi on ludedthat by in reasing the pile diameterthe stress bulb formed in front of the

pile is stret hed deeper into the soil.This results in a greater deformationdue to the same soil pressure at thepile. Terzaghi therefore postulatedthat the soil pressure a ting on thepile wall is linearly proportional tothe inverse of the pile diameter givingthat the modulus of subgrade rea -tion, Epy, is independent on the dia-meter.� Vesi (1961) proposed a relation be-tween the modulus of subgrade re-a tion used in the Winkler approa hand the soil and pile properties. Thisrelation showed that Epy is indepen-dent of the diameter for ir ular andsquared piles.� Pender (1993) refers to two reports ondu ted by Carter (1984) and Ling(1988). Assuming a simple hyper-boli soil model for the relationshipbetween soil resistan e and pile de-�e tion, they ba k al ulated values ofE∗

py and pu from �eld tests. In theba k al ulation they assumed thatYoung's modulus of elasti ity of thesoil and therefore also the intial sub-grade rea tion modulus were onstantwith depth. Based on the ba k al u-lations they proposed an expression ofE∗

py whi h is linearly proportional tothe pile diameter.Pender et al. (2007) omments on the re-sear h of Carter (1984) and Ling (1988)and their on lusion of E∗

py varying lin-early with pile diameter. Pender et al.(2007) questions the validity of a onstantvalue of Es with depth. Instead they pro-pose Es to be proportional to either thesquare root of the depth or to the depth.They suggests that the �ndings of Pender(1993) was due to a false assumption of thevariation of Young's modulus of elasti itywith depth. They, on lude that E∗

py isindependent of the pile diameter.The on lusions made by Terzaghi (1955)and Vesi (1961) on erns the subgrade re-

31a tion modulus, Epy, while the on lusionsmade by Pender (1993) on erns the intialmodulus of subgrade rea tion, E∗

py. The on lusions of Terzaghi (1955) and Vesi (1961) might also be appli able for the ini-tial modulus of subgrade rea tion, k, andthe initial sti�ness, E∗

py.Based on the investigations presented byTerzaghi (1955), Vesi (1961), Pender(1993), and Pender et al. (2007), it mustbe on luded that no lear orrelation be-tween the initial modulus of subgrade re-a tion and the pile diameter has been re-alised. Ashford and Juirnarongrit (2005) ontributed to the dis ussion with theirextensive study of the problem whi h wasdivided into three steps:� Numeri al modelling by means of asimple �nite element model.� Analyses of vibration tests on large-s ale on rete piles.� Ba k- al ulation of p�y urves fromstati load tests on the on rete piles.The �nite element analysis was a ordingto Ashford and Juirnarongrit (2005) verysimple and did not a ount very well forthe soil-pile intera tion sin e fri tion alongthe pile, the e�e t of soil on�nement, andgaps on the ba k of the pile were not in- luded in the model. In order to isolate thee�e t of the diameter on the magnitude ofEpy, the bending sti�ness of the pile waskept onstant when varying the diameter.The on lusion of the �nite element analy-sis were that the diameter had some e�e ton the pile-head de�e tion as well as themoment distribution. An in rease in dia-meter led to a de reasing pile-head de�e -tion and a de reasing depth to the pointof maximum moment. However, Ashfordand Juirnarongrit (2005) on luded thatthe e�e t of in reasing the diameter ap-peared to be relatively small ompared tothe e�e t of in reasing the bending sti�-ness, EpIp.

The se ond part of the work by Ashfordand Juirnarongrit (2005) dealt with vibra-tion tests on large-s ale monopiles. Thetests in luded three instrumented pileswith diameters of 0.6, 0.9, and 1.2 m (12m in length) and one pile with a diameterof 0.4 m and a length of 4.5 m. All pileswere ast-in-drilled-hole and made up ofreinfor ed on rete. They were installedat the same site onsisting of slightly ho-mogenous medium to very dense weakly emented layey to silty sand. The pileswere instrumented with several types ofgauges, i.e. a elerometers, strain gauges,tiltmeters, load ells, and linear poten-tiometers. The on ept of the tests werethat by subje ting the piles to small lat-eral vibrations, the soil-pile intera tion atsmall strains ould be investigated.Based on measured a elerations, the nat-ural frequen ies of the soil-pile systemwere determined. These frequen ies werein the following ompared to the naturalfrequen ies of the system determined bymeans of a numeri al model. Two di�er-ent expressions for the modulus of sub-grade rea tion, Epy, were used: one thatis linearly dependent; and one that is in-dependent on the diameter. The strongest orrelation was obtained between the mea-sured frequen ies and the frequen ies om-puted by using the relation independent ofthe diameter. Hen e, the vibration testssubstantiate Terzaghi and Vesi 's on lu-sions. It is noti ed that the piles wereonly subje ted to small de�e tions, hen eEpy ≈ E∗

py.Finally, Ashford and Juirnarongrit (2005)performed a ba k- al ulation of p�y urvesfrom stati load ases. From the ba k- al ulation a soil resistan e was found atthe ground surfa e. This is in ontrast tothe p�y urves for sand given by Reese etal. (1974) and the re ommendations inAPI (2000) and DNV (2010) in whi h theinitial sti�ness, E∗

py, at the ground surfa eis zero. The resistan e at the ground sur-fa e might be a onsequen e of ohesion in

32the slightly emented sand or a result ofmagni� ation of measurement un ertain-ties when double-di�erentiating the strain-gauge measurements.Furthermore, a omparison of the resultsfrom the ba k- al ulations for the variouspile diameters indi ated that the e�e tsof pile diameter on E∗

py were insigni� ant.The three types of analyses ondu ted byAshford and Juirnarongrit (2005) there-fore indi ate the same: the e�e t of thediameter on E∗

py is insigni� ant.Fan and Long (2005) investigated the in-�uen e of the pile diameter on the soil re-sponse by means of numeri al modelling.They employed the onstitutive modelproposed by Desai et al. (1991) and anon-asso iative �ow rule in their numer-i al model. By varying the diameter andkeeping the bending sti�ness, EpIp, on-stant in their �nite element model they in-vestigated the in�uen e of the pile diame-ter on the initial subgrade rea tion mod-ulus. The results are given as urves nor-malised by the diameter and verti al ef-fe tive stress as shown in �g. 26. No sig-ni� ant orrelation between diameter andinitial sti�ness is observed. It must be em-phasised that the investigation onsideredonly slender piles.For non-slender piles the bending sti�nessmight ause the pile to de�e t almost asa rigid obje t. Therefore, the de�e tionat the pile-toe might ause a signi� antsoil resistan e near the pile toe. Thus a orre t predi tion of the variation of initialsti�ness with depth is important in orderto determine the orre t pile de�e tion.Based upon a design riterion demand-ing the pile to be �xed at the toe, LesnyandWiemann (2006) investigated by ba k- al ulation the validity of the assumptionof a linearly in reasing E∗

py with depth.The investigation indi ated that E∗

py isoverestimated for large-diameter piles atgreat depths. Therefore, they suggesteda power fun tion, to be used instead of a

Figure 26: E�e t of hanging the diameter, afterFan and Long (2005).linear relation, f. �g. 27. A �nite ele-ment model was made in order to validatethe power fun tion. The investigationsshowed that employing the power fun -tion approa h gave de�e tions more simi-lar to the numeri al modelling than by us-ing the traditional linear approa h in thep�y urve method. However, it was em-phasised that the method should only beused for determination of pile length. Thep�y urves still underestimates the pile-head de�e tions even though the paraboli approa h is used.The above mentioned investigations allmade by means of ohesionless soils aresummarised in tab. 4. From this tabularit is obvious that more resear h is needed.Looking at ohesive materials the testsare also few. A ording to Ashford

33Table 4: Chronologi al list of investigations on erning the e�e ts of diameter on the initial sti�ness of the p�y urveformulations.Author Method Con lusionTerzaghi (1955) Analyti al IndependentVesi (1961) Analyti al IndependentCarter (1984) Analyti al expression alibratedagainst full-s ale tests Linearly dependentLing (1988) Validation of the method proposedby Carter (1984) Linearly dependentAshford and Juirnarongrit (2005) Numeri al and large-s ale tests Insigni� ant in�uen eFan and Long (2005) Numeri al Insigni� ant in�uen eLesny and Wiemann (2006) Numeri al Initial sti�ness isnon-linear for longand large-diameter pilesPender et al. (2007) Analyti al expression alibratedagainst full-s ale tests Independent* *

aparabolic ref

py pyref

xE Ex

æ ö= ×ç ÷ç ÷è ø

*linearpyE k x= ×

refx

*refpyE *

pyE

Dep

th

Initial stiffnessFigure 27: Variation of initial sti�ness, E∗

py,as fun tion of depth, after Lesny and Wiemann(2006). The linear approa h is employed in Reeseet al. (1974) and the design odes, e.g. API (2000)and DNV (2010). The exponent a an be set to0.5 and 0.6 for dense and medium dense sands,respe tively.

and Juirnarongrit (2005) the most signif-i ant �ndings are presented by Reese etal. (1975), Stevens and Audibert (1979),O'Neill and Dunnavant (1984), and Dun-navant and O'Neill (1985).Reese et al. (1975) ba k- al ulated p�y urves for a 0.65 m diameter pile in orderto predi t the response of a 0.15 m pile.The al ulations showed a good approx-imation of the moment distribution, butthe de�e tions however were onsiderablyunderestimated ompared to the measuredvalues asso iated with the 0.15 m test pile.Based on published lateral pile load testsStevens and Audibert (1979) found thatde�e tions omputed by the method pro-posed by Matlo k (1970) and API (1987)were overestimated. The overestimationin reases with in reasing diameter leadingto the on lusion that the modulus of sub-grade rea tion, Epy, in reases for in reas-ing diameter.By testing laterally loaded piles with di-ameters of 0.27 m, 1.22 m, and 1.83 m inan over onsolidated lay, O'Neill and Dun-navant (1984) and Dunnavant and O'Neill(1985) found that there were a non-linearrelation between de�e tion and diameter.They found that the de�e tion at 50 %

34of the ultimate soil resistan e generallyde reased with an in rease in diameter.Hen e, Epy in reases with in reasing pilediameter.Kim and Jeong (2011) and Jeong et al.(2011) investigated the e�e t of pile dia-meter on the initial sti�ness through nu-meri al modelling. They onsidered pilessituated in lay. They found that the in-tial sti�ness of the p�y urves in reases lin-early with the square root of the pile dia-meter.4.6 Choi e of horizontal earthpressure oe� ientWhen al ulating the ultimate soil resis-tan e by method A the oe� ient of hor-izontal earth pressure at rest, K0, equals0.4 even though it is well-known that therelative density/the internal fri tion anglein�uen es the value of K0. In addition,pile driving may in rease the oe� ient ofhorizontal earth pressure K.The in�uen e of the oe� ient of horizon-tal earth pressure, K, is evaluated by Fanand Long (2005) for three values of K andan in rease in ultimate soil resistan e werefound for in reasing values of K. The in- rease in ultimate soil resistan e is due tothe fa t, that the ultimate soil resistan e isprimarily provided by shear resistan e inthe sand, whi h depends on the horizontalstress.Reese et al. (1974), and O'Neill andMur hison (1983) and thereby also API(2000) and DNV (2010) onsider the initialmodulus of subgrade rea tion k to be in-dependent of K. Fan and Long (2005) in-vestigated this assumption. An in rease inK results in an in rease in on�ning pres-sure implying a higher sti�ness. Hen e, kis highly a�e ted by a hange in K su hthat k in reases with in reasing values ofK.

4.7 Shearing for e at the pile-toeRe ently installed monopiles have diame-ters around 4 to 6 m and a pile slender-ness ratio around 5. Therefore, the bend-ing sti�ness, EpIp, is quite large omparedto the pile length. The pile urvature willtherefore be small and the pile will almostbehave as a rigid obje t as shown in �g.28.

Figure 28: De�e tion urve for non-slender pile.As shown in �g. 28 there is a signi� antnegative de�e tion at the pile-toe. Thisde�e tion auses shearing stresses at thepile-toe to o ur, whi h in rease the totallateral resistan e. A ording to Reese andVan Impe (2001) a number of tests havebeen made in order to determine the shear-ing for e at the pile-toe, but urrently noresults from these tests have been pub-lished and no methods for al ulating theshearing for e as a fun tion of the pile toede�e tion have been proposed.Due to rigid pile behaviour normal stressesat the pile toe will in�i t a bending mo-ment on the pile toe resulting in a big-ger pile sti�ness and apa ity. Resear h isneeded to establish a relationship betweenthe pile toe rotation and the applied mo-ment at the pile toe.

354.8 Shape of p�y urvesCurrently, a tangent hyperboli fun tionis employed to des ribe the shape of p�y urves for piles in sand, f. (29) andO'Neill and Mur hison (1983). Othershapes of p�y urves has also been pro-posed to des ribe the relationship betweenthe soil resistan e a ting on the pile walland the pile de�e tion, for instan e, Reeseet al. (1974), S ott (1980), PHRI (1980),and Carter (1984). Reese et al. (1974)suggested the use of a pie ewise urve onsisting of an initial straight line, aparabola, and a straight line. These three urves were assembled into one ontinuouspie ewise di�erentiable urve, f. MethodA. S ott (1980) proposed a p�y urve forsand onsisting of two straight lines. Hisre ommendation was based on entrifugetests of laterally loaded piles. The ex-pression of S ott (1980) is not boundedby an upper limit. Hen e, the ultimatesoil resistan e is not onsidered in thatmethod. Mur hison and O'Neill (1984) ompared these three expressions with aseries of �eld tests on �exible piles andfound the tangent hyperboli fun tion to�t best with the tests. Carter (1984) pro-posed the use of a hyperboli expressionfor p�y urves in sand:

p(y)n =y

1/E∗

py + y/pnu(45)where n is a dimensionless onstant.Carter (1984) proposed to use n = 1 forsand and n = 0.2 for lay. Ling (1988) on-�rmed the hyperboli expression by om-parison with 28 full-s ale tests on �exiblepiles.PHRI (1980) proposes the use of a p�y urve formulation in whi h the soil resis-tan e is proportional with the square ofthe pile de�e tion. Hen e, this p�y urveformulation is not bounded by an upperlimit. Terashi (1989) found a good agree-ment between this p�y urve expression

and entrifuge tests on �exible piles sit-uated in dense sand.The a ura y of the p�y urves proposedby O'Neill and Mur hison (1983), Carter(1984), and PHRI (1980) needs to be om-pared and validated for non-slender piles.4.9 Layered soilThe p�y urve formulations of Reese etal. (1974), Mur hison and O'Neill (1974),et . onsiders piles situated in homoge-neous soil. However, the soil strati� a-tion is rarely homogeneous. A few an-alyti al studies on the e�e t of layeredsoils have been ondu ted, for instan e,Davisson and Gill (1963), Khadilkar et al.(1973), Naik and Peyrot (1976), and Dordi(1977). However, these analyses do not onsider the non-linearity of the soil.Georgiadis (1983) proposed a new ap-proa h to develop p�y urves in a layeredsoil strati� ation. The approa h involvesthe determination of an equivalent depth,h, for all soil layers existing below the up-per soil layer. The equivalent depth oflayer i is determined by solving hi in thefollowing equation:

F1 + ...+ Fi−1 = Fi ⇒ (46)∫ H1

0pudx+ ...+

∫ hi−1+Hi−1

hi−1

pudx =

∫ hi

0pudx (47)where F1 is the sum of the ultimate soil re-sistan e for layer 1, Fi−1 is the sum of theultimate soil resistan e for the (i − 1)'th,and Fi is the sum of the ultimate soil re-sistan e for the i'th layer. H1, Hi−1, and

Hi are the layer thi kness of soil layer 1,i − 1, and i, respe tively. hi−1 and hi arethe equivalent depth of the soil layers i−1and i.

36Georgiadis (1983) validated his methodagainst a �eld test at Lake Austin on apile with a diameter of 0.152 m and anembedded pile length of 4.9 m. Hen e, thelength to diameter ratio was 32.2 and thepile an be onsidered as �exible. The soilstrati� ation at the site onsisted of 0.38m of sti� lay overlying a medium densesand layer. The proposed method for lay-ered soil �tted the �eld test very well.It should be emphasized that the methodof Georgiadis (1983) for deriving p�y urves for layered soils is developed andvalidated for �exible piles. The methodstill needs validation for piles behavingrigidly.Based on numeri al analyses Yang andJeremi (2005) as well as M Gann et al.(2012) investigated laterally loaded pilessituated in a layered soil strati� ation.Yang and Jeremi (2005) modelled thebehaviour of a �exible square pile situ-ated in a strati� ation of sand and soft lay. They ondu ted numeri al simula-tions with both a sand- lay-sand and a lay-sand- lay strati� ation. The analysisof M Gann et al. (2012) is based on ir u-lar piles situated in seismi areas exposedto lateral spreading. They onsidered pilesinstalled in sands with a loose liqui�ed in-termediate layer.Yang and Jeremi (2005) used von Mises onstitutive model to model the lay andthe Dru ker-Prager onstitutive model forthe sand. They modelled a pile with awidth of 0.429 m and a length of 13.7m. Hen e, the slenderness ratio was 31.9.Similar to Georgiadis (1983) they foundthat the upper layers a�e ted the p�y urves of the lower layers. Further, theyfound that the lower layers also a�e tedthe p�y urves of the upper layers in su ha way that the p�y urves of a sti� upperlayer are redu ed near a soft intermediatelayer. The size of the redu tion was foundto depend on the distan e to the interlayer,su h that the largest redu tion took pla e

at the interlayer. For the lay-sand- laystrati� ation they found that the sti� in-termdiate layer resulted in in reased soilresistan e in the upper lay layer.M Gann et al. (2012) used the Dru ker-Prager onstitutive model in their numer-i al model. They modelled a ir ular pilewith a diameter varying from 0.61 m to2.5 m. Similar to Yang and Jeremi (2005)they found that the intermediate layer af-fe ts the soil resistan e of the upper layer.A ording to M Gann et al. (2012) thesti� soil near the interfa e of the weakerintermediate layer an be pushed into theweaker layer as the pile de�e ts laterally.This explains the redu tion in the soil re-sistan e of the sti� soil layers.Based on their numeri al simulations, M -Cann et al. (2012) presented an expres-sion for the redu tion of the soil resistan eof the upper and lower layer. The redu -tion depends exponentially on the distan efrom the intermediate layer. Other pa-rameters su h as the pile diameter, thedepth of the intermediate layer, the fri -tion angle of the upper and lower layers,and the thi kness of the intermediate layerwere also in luded in the expression forthe redu tion. The analysis of M Gannet al. (2012) onsidered the intermedi-ate layer as lique�ed. Their expression istherefore only validated for strati� ationswith an intermediate layer whi h is lique-�ed. The expression might however alsobe valid in strati� ations where the inter-mediate layer is signi� antly softer thanthe upper and lower layers, for instan estrati� ations with an organi intermedi-ate layer.4.10 Long-term y li loadingO�shore wind turbines are exposed to y li loading from the wind and wavefor es. During the lifetime of an o�shorewind turbine the foundation will be ex-posed to a few number of load y les with

37large amplitudes due to storms and fur-ther to 106-108 load y les with low or in-termediate amplitudes. The ratio betweenthe minimum and maximum load in ea h y le, ζc, will vary with time. The ratio be-tween the maximum load in ea h y le andthe stati pile apa ity is in the followingdenoted as ζb. When designing monopilefoundations for o�shore wind turbines itshould be ensured that the a umulatedpile rotation is less than the value spe i�edby the wind turbine supplier. Similarly,it should also be ensured that the nat-ural frequen y of the ombined stru tureis within the range spe i�ed by the windturbine supplier. Typi ally, the founda-tion is designed su h that the natural fre-quen y of the ombined stru ture is withinthe rotor frequen y and the blade passingfrequen y. A ording to LeBlan (2009),wind turbines are often designed su h thatthe rotor frequen y is in the range of 0.17-0.33 Hz, while the blade passing frequen ytypi ally is in the range of 0.5-1.0 Hz. Theenergy ri h wind turbulen e lies below afrequen y of 0.1 Hz, and the frequen y ofextreme waves is typi ally in the rangeof 0.07-0.14 Hz. When a pile is exposedto y li loading, the sti�ness of the soilmight hange due to a re on�guration ofthe soil parti les. Therefore, knowledgeregarding the in�uen e of y li loadingon the sti�ness of the soil-pile intera tionis ne essary for a urate determination ofthe a umulated pile rotation and of thevariation of the natural frequen y for the ombined stru ture with time.The p�y urve formulations proposed byReese et al. (1974) and O'Neill andMur hison (1983) a ounts for y li load-ing by means of redu tions of the empiri alfa tors A and B. Hen e, the a umulatedpile de�e tion is a ounted for, however, ina very simpli�ed manner. Changes in theinitial sti�ness of the p�y urves is not a - ounted for, sin e A only a�e t the upperlimit of soil resistan e (Method A and B),and B the soil resistan e at a pile de�e -tion of y = D/60 (Method A). The param-

eters A and B for y li loading are basedon few tests on �exible piles with up toapproximately 100 load y les. Further,the in�uen e of relative density, installa-tion method, number of y les, et . arenot in luded in the expression of A and Bfor y li loading. Hen e, these p�y urveformulations are in omplete in des ribingthe y li pile behaviour of monopile foun-dations for o�shore wind turbines.The behaviour of laterally loaded pilessubje ted to y li loading has been inves-tigated by means of experimental testingand numeri al modelling. The major �nd-ings are summarised in the following. Thepile and soil properties as well as load-ing onditions for the experimental test-ing whi h is referred to regarding the be-haviour of y li ally loaded piles are sum-marised in tab. 5.Long and Vanneste (1994) summarisesprevious resear h regarding the behaviourof y li ally loaded piles:� Prakash(1962), Davisson and Salley(1970), and Alizadeh and Davisson(1970) onsidered the y li pile re-sponse based on model and �eld tests.Prakash (1962) and Davisson and Sal-ley (1970) ondu ted model tests onaluminium pipe piles with outer di-ameters of 12.7 mm (0.5 in) and em-bedded pile lengths of 0.533 m (21in). Hen e the slenderness ratio is40 and the piles an be onsideredas �exible. The piles were situatedin medium dense dry sand. Alizadehand Davisson (1970) ondu ted �eldtests on a pile with an outer diame-ter of 0.4 m and a slenderness ratio of40. The pile was situated in a layeredsoil onsisting of silty sand to grav-elly sand. Prakash (1962), Davissonand Salley (1970) as well as Alizadehand Davisson (1970) on luded thatfor 50 or more load y les the y li sti�ness of the modulus of subgraderea tion is approximately 30 % of the

38Table 5: Pile, soil and loading properties for the model and �eld tests used for investigation of the behaviour of y li ally loaded piles. Pile Embedded Slenderness Soil ζb ζc Ndiameter pile length ratio ompa tionD L L/D[m℄ [m℄ [-℄ [-℄ [-℄ [-℄Cox et 0.61 21.0 34 medium dense (-1)- 0-100al. (1974)/ to very dense (-0.25)Reese etal. (1974)Prakash 0.0127 0.533 40 Medium 100(1962) denseDavisson and 0.0127 0.533 40 Medium 4Salley (1970) denseAlizadeh and 0.400 16 40 Loose 0 100Davisson (1970)Little and 0.510- 29.6- 32-60 Medium 0- 21Briaud (1988b) 1.065 39.0 dense 0.5Long and 0.145- 3.8- 3-84 Loose to (-1.0)- 5-Vanneste (1994) 1.430 39.0 dense 0.5 500Lin and 0.145- 5.0- 4-84 Loose to (-1.0)- 4-Liao (1999) 1.430 21.0 dense 0.1 100Peng et 0.0445 0.400 9 Medium 0.2- (-1)- 10000al. (2006) dense 0.6 (-0.6)Peralta and 0.060- 0.200- 3-8 Medium 0 10000A hmus (2010) 0.063 0.500 denseLeBlan et 0.080 0.360 4.5 very loose 0.20- (-1.0)- 7000-al. (2010a) to loose 0.53 1.0 65000LeBlan et 0.080 0.360 4.5 very loose 0.28- 0 100-al. (2010b) to loose 0.53 10000stati sti�ness.� Broms (1964) similarly onsidered the y li pile behaviour based on thesubgrade rea tion method. He foundthat the degradation of the stati sti�ness depends on the relative den-sity of the soil, su h that the sti�-ness is redu ed to 25 % of the sta-ti sti�ness for loose soils and to 50% for dense soils. The mentioned re-du tions in subgrade rea tion modu-lus was for 40 load y les.� Little and Briaud (1988b) proposedto degrade the soil resistan e in the

p�y urve formulation with the num-ber of load y les by means of an ex-

ponential expression: pc = psN−a.The y li soil resistan e is denoted

pc, the stati soil resistan e is denotedps, the number of load y les is de-noted N and a is an empiri al fa tor.The expression was validated against12 pressuremeter tests on model pileswith outer diameters of 34.5 mm (1.36in) situated in dry sand. Further,the expression was validated againstsix �eld tests on pipe piles driven ordrilled into the soil. The piles hadouter diameters of 0.510 m to 1.065 m,embedded pile lengths of 29.6 to 39.0m and slenderness ratios of 32 to 60.The piles therefore exhibited a slen-der pile behaviour. The pile slender-

39ness ratio varied from 37 to 59. Thepiles were installed in medium densesand.Long and Vanneste (1994) analysed 34�eld tests on piles exposed to y li lat-eral loading. The pile dimensions wereD = 0.145 − 1.43 m, Lp = 3.8 − 39.0 m,Lp/D = 3−84. Various pile ross-se tionsand installation methods were used for the34 �eld tests. The soil ompa tion var-ied from loose to dense and the number ofload y les varied from 5 to 500. Based onba k-analyses of the �eld tests, they pro-posed to degrade the stati p�y urve for-mulation proposed by Reese et al. (1974)in the following way to a ount for y li loading:

pN = p1 ∗N−0.4t (48)

yN = y1 ∗N0.6t (49)where pN is the soil resistan e after N y- les, p1 is the stati soil resistan e, yN isthe pile de�e tion after N y les, y1 is thestati pile de�e tion, and t is a dimension-less parameter. The dimensionless param-eter t was found to depend primarily on

ζc, but also the installation method andthe relative density were found to exhibita minor in�uen e on t. They found thatt assumes the largest values for one-way y li loading with ζc = 0.0 − 0.5.Lin and Liao (1999) proposed a method fordetermination of the a umulated pile dis-pla ement aused by mixed lateral load-ing. Their method is based on the expres-sion for the umulative strains due to mix-ing of di�erent amplitude loads proposedby Stewart (1986) and on Miner's rule(Miner, 1945). In their method, they as-sume that the representative lateral strain an be al ulated from the pile de�e tionas ǫ = y/(2.5D). This relationship be-tween the lateral strain and the pile de�e -tion was originally suggested by Kagawaand Kraft (1980). Lin and Liao (1999)suggest that the relationship, Rs, betweenthe lateral strain after N y les, ǫN , and

the lateral strain after one y le, ǫ1, isgiven as:Rs =

ǫNǫ1

= 1 + t ln(N) (50)where t depends on the relative density,the installation method, ζc and the ratiobetween the pile length and the pile/soilrelative sti�ness, T . They alibrated theparameter t against 20 �eld tests on pileswith outer pile diameters of 0.145-1.43 m,embedded pile lengths of 5.0-21.0 m andslenderness ratios of 4-84. The installa-tion method varied and further the soil ompa tion varied from loose to dense.They validated their method against the�eld tests presented by Little and Briaud(1988b). A reasonable agreement werefound with the tests. It should be notedthat the number of load y les in the �eldtests were limited to a maximum of 100 y les.Peng et al. (2006) invented a new test-ing devi e for y li loading of laterallyloaded piles. By means of the new test-ing devi e they ondu ted two-way y li tests with 10000 y les and both balan edand unbalan ed y li loading. They on- entrated on the development of the inno-vative testing devi e and only presentedfew results from y li load tests. Thetest results they presented were for a pilewith an outer diameter of 44.5 mm, an em-bedded pile length of 400 mm and a slen-derness ratio of 9. The pile was situatedin a dry sand with ID = 71.7 %. Theloading frequen y were varied from 0.45-0.94 Hz. The applied y li loading hadζb = 0.2 − 0.6 and ζc = (−1) − (−0.6).They on luded that the pile displa ementin reases for in reasing loading frequen y.Whether this was due to resonan e be-tween the natural frequen y of the pile andthe loading was not dis ussed. They foundthat the a umulated pile displa ement issigni� antly greater for unbalan ed load-ing than balan ed loading, whi h is simi-lar to the �ndings of Long and Vanneste(1994) and Lin and Liao (1999). Further,

40they found that within 10000 load y lesthe a umulated pile de�e tion ontinuedto in rease.Lesny and Hinz (2007) proposed to mo-del the y li pile behaviour by means ofa ombination of �nite element modellingand y li triaxial testing. They imple-mented the results from undrained, un- onsolidated, stress- ontrolled y li triax-ial tests in the onstitutive model. Themethod for the �nite element modelling ofthe y li pile behaviour in ludes the fol-lowing steps:� At �rst the variation of load versusnumber of load y les is estimated.The loading is divided into a numberof load levels ea h with a orrespond-ing number of load y les.� For varying load levels the indu edstates of stresses in the soil is al u-lated by �nite element analysis usingsoil parameters for stati loading.� Triaxial tests are ondu ted a ordingto the determined stress onditions.� The a umulated plasti strain perload level is al ulated, and their sumis determined with use of Miner's rule(Miner, 1945).� The soil properties are modi�ed to a - ount for the y li behaviour, andthe pile behaviour is determined bymeans of �nite element modelling em-ploying the updated soil parameters.The method proposed by Lesny and Hinz(2007) needs to be validated against y li tests on laterally loaded piles.A hmus et al. (2009b) analysed the y li pile behaviour of non-slender large-diameter piles through numeri al mod-elling employing the Mohr-Coulomb on-stitutive model. The y li behaviourofthe soil was implemented through a de-grading soil sti�ness. The formulation

proposed by Huurman (1996), whi h isbased on triaxial testing of ohesionlesssoil, was applied to express the sti�nessdegradation. A hmus et al. (2009b) pre-sented a parametri al study on the a u-mulation of pile de�e tion due to y li loading in whi h the pile diameter, thepile length, the loading e entri ity, therelative density and ζb was varied withinD = 2.5 − 7.5 m, L = 20 − 40 m, e =0 − 40 m, medium dense to dense sandand ζb = 0 − 0.6. For all the simulationsone-way loading with ζc = 0 were applied.Based on the parametri study they pre-sented design harts relating the ratio be-tween the stati and y li pile de�e tion(a umulation rate of deformation) with ζbfor varying numbers of load y les. Theyfound that the pile diameter, the embed-ded pile length, and the relative soil den-sity a�e t the a umulation rate of defor-mation through their e�e t on the stati pile apa ity and hen e also their e�e t onthe normalized load.Peralta and A hmus (2010) ondu ted aseries of 1-g tests on both �exible andrigid piles in order to investigate the be-haviour of y li loaded piles. The piledimensions was D = 60 − 63mm andL = 200 − 500mm. The pile material em-ployed for the tests varied from steel tohigh density poly-ethylene (HDPE). Thepiles made of HDPE behaved as slenderpiles due to the signi� antly lower Young'smodulus of elasti ity for HDPE. One-way y li loading with ζc = 0 were onsid-ered. For ea h test, the 10000 load y leswere applied. They attempted to �t bothan exponential and a logaritmi expres-sion for the a umulation of displa ementto the test results, as proposed by Longand Vanneste (1994) and Lin and Liao(1999), respe tively. They on luded thatthe exponential fun tion for the displa e-ment a umulation �tted well with the ex-perimental tests on rigid piles while thelogarithmi expression �tted the �exiblepiles well. They presented a omparison ofthe evaluation of a umulated pile de�e -

41tion for two equivalent irregular load pat-terns: one in whi h the y li load ampli-tude as ended; and one in whi h the y li load amplitude des ended. From the om-parison it ould be observed that the a - umulated load displa ement was approxi-mately 25 % higher for the irregular y li load pattern with as ending loads than thepattern with des ending loads.LeBlan et al. (2010a) and LeBlan et al.(2010b) investigated the y li behaviourof non-slender piles through small-s aletesting at 1-g. They tested a pile with anouter diameter of 80 mm and an embeddedpile length of 360 mm. The slenderness ra-tio was hereby 4.5 implying rigid pile be-haviour. They ondu ted tests at relativesoil densities of 4 and 38 %. The pile wasexposed to a series of y li load tests withvarying ζb and ζc. ζb was varied between0.2 and 0.53, while ζc was varied from -1to 1. The values of ζb orresponds to loadsranging from the fatigue limit state (FLS)to the servi eability limit state (SLS).LeBlan et al. (2010a) onsidered the a - umulated pile rotation and the hangein pile sti�ness for ontinouos long-term y li loading. Regarding the a umulatedpile rotation, they proposed the followingexpression:∆θ(N)

θs= Tb(ζb,ID)Tc(ζc)N

0.31 (51)where Tb and Tc are dimensionless fun -tions. They found that Tb in reases forin reasing values of both ζb and ID, whilethey proposed a nonlinear variation of Tcwith ζc. For ζc equal to either -1 or 1, e.i.two-way y li loading with a mean valueof 0 and stati loading, respe tively, theysuggested that Tc is 0, while for ζc = 0, thedimensional fun tion Tc assumes a value of1. The maximum value of Tc was proposedto 4 at ζc = −0.6, whi h implies that two-way y li loading with ζc = −0.6 give riseto signi� antly larger pile rotations thanone-way y li loading.

In LeBlan et al. (2010a) also the varia-tion of pile sti�ness, k = M/θ, was inves-tigated. They found that the pile sti�nessin reases with the number of load y les,and further that the in rease is indepen-dent of fa tors su h as ζb, ζc, and ID. Itseems questionable that the relative den-sity should have no in�uen e on the in- rease in pile sti�ness. Therefore y li tests at higher values of relative densityare needed to further extrapolate the �nd-ings from LeBlan et al. (2010a).LeBlan et al. (2010b) investigated the a - umulated pile rotation for piles exposedto random y li loading. They found thatthe sequen e of loading has no signi� antin�uen e on the a umulated pile rotation.Further, they found that the number of y- les to neutralise N reversal load y les ismore than N . Based on that they on- luded that onservatively it an be as-sumed that N load y les are ne essary toneutralise N reversal load y les. Basedon the experimental tests they proposed amethod to a ount for random y li load-ing in the determination of the a umu-lated pile rotation. They suggested to di-vide a time-series of random y li loadinginto a number of load sequen es by meansof the extended rain�ow method proposedby Ry hlik (1987). The a umulated pilerotation of the the i'th load sequen e, θi, an then be determined by means of thefollowing equations:∆θi =((∆θi−1)

1/0.31

+ (θsTbTc)1/0.31i Ni)

0.31 (52)θi =∆θi +max(θs,1,...,θs,i) (53)where the subs ript i denotes the i'th loadsequen e. The equations are based on the�ndings in LeBlan et al. (2010a) andMiner's rule (Miner, 1945).A hmus et al. (2010a) validated the nu-meri al model proposed by A hmus et al.(2009b) against the small-s ale tests re-ported by LeBlan et al. (2010a). Areasonable agreement between the numer-i al model and the experimental �ndings

42were found. However, further validation ofthe numeri al model is needed. It shouldbe noted that the y li soil behaviourwhi h they assumed in their numeri al mo-del was not based on the sand materialemployed in the tests by LeBlan et al.(2010a).SummaryThe e�e t of ontinouos long-term y li loading on the a umulated pile rota-tion/de�e tion has been investigated ex-perimentally for both slender and non-slender piles. For slender piles severalmodel and �eld tests have been reportedin the litterature. The number of load y les have however for the majority ofthese tests been less than 100. For non-slender piles the experimental resear h onthe y li pile behaviour relies on modeltests. The majority of the resear hers pro-pose an exponential relationship betweenthe number of y les and the a umulatedpile rotation. However, the resear h re-veals opposing on lusions regarding thee�e t of the relative density on the ex-ponent relating the pile rotation with thenumber of y les.The e�e t of ontinouos long-term y li loading on the pile behaviour has been in-vestigated through numeri al modelling inwhi h the soil sti�ness is degraded basedon triaxial tests (Lesny and Hinz, 2007;and A hmus et al., 2009b). The prospe tof degrading the soil sti�ness in the onsti-tutive models on the basis of triaxial test-ing is an interesting idea. However, valida-tion against experimental work (preferably�eld tests) is needed.Only few experimental pile tests have been ondu ted regarding the a umulated pilerotation for random long-term y li load-ing. LeBlan et al. (2010b) found thatthe a umulated pile rotation is indepen-dent of the loading sequen e, whi h dis-agrees with the �ndings of Peralta and

A hmus (2010). The in�uen e of loadingsequen e needs to be further investigated.LeBlan et al. (2010b) proposed a methodfor determination of the a umulated pilerotation based on the extended rain�owmethod proposed by Ry hlik (1987) andMiner's rule.Resear h regarding the variation of thesti�ness of the soil-pile intera tion withlong-term y li loading is needed. Re-sults from LeBlan et al. (2010a) indi- ate that the sti�ness in reases logarith-mi ally with the number of y les and thatthe in rease is independent of the relativedensity. However, the tests were only on-du ted in loose to medium dense soil, andhen e a further investigation is needed fordense to very dense soil.4.11 S our e�e t on the soil-pileintera tionAround a verti al pile pla ed on the seabedthe water-parti le �ow from urrents andwaves will undergo substantial hanges ausing erosion of soil material. Hen e,lo al s our holes around these piles willform. When large wind farms are built,s ouring an also take pla e on a moreglobal s ale. The s our depth of lo als our holes an a ording to DNV (2010)be up to 1.3 times the pile diameter.S our prote tion onsisting of ro k in�ll an be employed to avoid the developmentof s our. However, s our prote tion is veryexpensive and on some lo ations it anbe hard to deploy due to the sea ondi-tions. Det Norske Veritas provide regu-lations for the possible depths of globaland lo al s our holes (DNV, 2010). Fur-ther, they require that the p�y urves aremodi�ed for the presen e of s our. How-ever, they do not provide any regulationson how to modify the p�y urves for thepresen e of global and lo al s our.The International Organization for Stan-dardization, ISO, and the Ameri an

43

Figure 29: Redu tion in e�e tive verti al stresses and initial sti�ness of the p�y urves due to globaland lo al s our, after ISO (2007).Petroleum Institute, API, provides a sim-ple method to a ount for lo al and globals our in the p�y urve formulation (ISO,2007; API, 2008) in whi h the e�e tiveverti al stresses are assumed to vary withdepth as shown in �g. 29. The hange ine�e tive verti al stress hanges the valueof the ultimate soil resistan e, f. (28).They only redu e the initial sti�ness of thep�y urves due to the presen e of globals our. In ISO (2007) and API (2008) it isstated that the method shown in �g. 29 isnot generally a epted.When lo al and global s our takes pla e,the e�e tive soil stresses de rease. Hen e,the soil be omes slightly over onsolidated,with the largest over onsolidation ratio inthe upper soil layers. As the soil be- omes over onsolidated the soil strengthin reases. Hen e, it is onservative notto take the over onsolidation e�e t intoa ount. Lin et al. (2010) modi�ed thep�y urve formulation proposed by Reeseet al. (1974) to a ount for the e�e t ofover onsolidation. Due to the over onsol-idation the oe� ient of horizontal earthpressure in reases, and further, the fri -tion angle in reases. These hanges in thesoil properties were in orporated in the ex-pression of pu, f. (12) and (13). They

ompared the pile behaviour al ulated bymeans of a Winkler model approa h forthe test piles at Mustang Island, f. Coxet al. (1974), for two onditions: one inwhi h the original fri tion angle and o-e� ient of horizontal earth pressure wereused; and one in whi h the over onsoli-dated parameters were used. They founda signi� ant in rease in pu when the soilis onsidered to be over onsolidated. Fur-ther, the maximum bending moment inthe pile de reased with 7 % when assum-ing over onsolidated soil. Hen e, for pilesinstalled without s our prote tion, the ef-fe t of over onsolidation should be in or-porated in the design.A hmus et al. (2010b) ondu ted a nu-meri al study of the e�e t of s our on thelateral pile behaviour of non-slender large-diameter piles. They employed the om-mer ial program ABAQUS and the Mohr-Coulomb onstitutive model. They in or-porated y li soil behaviour by means ofthe degradation sti�ness method (A hmuset al., 2007; Kuo, 2008). They varied pa-rameters su h as the pile diameter, thes our depth, and the loading e entri ity.They on luded that, the e�e t of s our in- reases for de reasing pile slenderness ra-tio. Further, they found that s our is more

44unfavourable for small loading e entri i-ties.Due to hanging sea onditions the s ourdepth around unprote ted monopile foun-dations will vary with time. The pro essin whi h the s our depth is de reasing istermed ba k�lling. Currently, there is noknowledge regarding the properties of theba k�lled soil material and how to in or-porate this in a Winkler approa h. Knowl-edge regarding these issues are importantfor the fatigue design of the steel materialused for the monopile.5 Con lusionMonopiles are an often used foundation on ept for o�shore wind energy onvert-ers. They are usually designed by use ofthe p�y urve method whi h is a versa-tile and pra ti al design method. Further-more, the method has a long history ofapproximately 50 years of experien e.The p�y urve method was originally de-veloped to be used in the o�shore oil andgas se tor and has been veri�ed for �exi-ble piles with pile diameters up to approx-imately 2 m. However, for o�shore windturbines, monopiles with diameters of 4 to6 m and a slenderness ratio around 5 arenot unusual.In the present review a number of the as-sumptions and not lari�ed parameters as-so iated with the p�y urve method havebeen des ribed. The analyses onsideredin the review state various on lusions ofwhi h some are rather ontradi tory. Im-portant �ndings of this paper are sum-marised as follows:� When employing the Winkler modelapproa h, the soil response at a givendepth is assumed to be independent ofthe de�e tions above and below thatgiven depth. Pasternak (1954) pro-posed a modi� ation of the Winkler

model approa h in whi h the shearstress between soil layers is a ountedfor. However, the e�e t of involvingthe shear stress between soil layersseems to be rather small, and fromthe analysis it is not lear whether theresults are dependent on pile proper-ties.� The failure modes assumed whendealing with the ultimate soil resis-tan e at shallow depth seems ratherunrealisti . In the traditionally em-ployed methods the surfa e of the pileis assumed smooth. Furthermore, themethod does not take the pile de-�e tion pattern into a ount, whi hseems riti al for rigid piles.� Soil dilatan y a�e ts the soil responsesu h that a large value of the dila-tan y angle leads to large values of theultimate soil resistan e. The e�e t ofsoil dilatan y is negle ted in the p�y urve formulations. However, a re-lationship between the soil dilatan yand the fri tion angle exists. Hen e,the in�uen e of soil dilatan y is im-pli itly a ounted for in the expres-sions for pu.� Determining the ultimate soil resis-tan e by the method proposed byHansen (1961), seems to give morereasonable results than the methodasso iated with the design odes.Prasad and Chari (1999) presentedan expression for the ultimate soil re-sistan e whi h a ounts for the de-�e tion pattern for non-slender piles.Zhang et al. (2005) modi�ed the ex-pression of Prasad and Chari (1999)su h that side fri tion is in luded.Large-s ale tests are needed to fur-ther validate the expressions for theultimate soil resistan e.� In urrent pra ti e, piles are analysedseparately for verti al and horizontalbehaviour. The e�e t on ombinedloading has untill now primarily been

45investigated by means of numeri almodelling. From this numeri al workit an be on luded that verti al load-ing a�e ts the horizontal pile sti�nessand apa ity. Compressional verti alloading has a minor positive e�e t onthe horizontal sti�ness and apa ity,while tensile verti al loading de reasethe lateral pile apa ity moderately.The e�e t of ombined loading on theverti al sti�ness and apa ity is moresigni� ant.� Analyses of the sensitivity of p�y urves to pile bending sti�ness, EpIp,gives rather ontradi tory on lu-sions. A ording to the Strain Wedgemodel, the formulations of p�y urvesare highly a�e ted by the pile bend-ing sti�ness. This is in ontradi tionto the existing p�y urve formulationand the numeri al analyses performedby Fan and Long (2005) as well asKim and Jeong (2011).� The initial sti�ness is independent ofpile diameter a ording to the exist-ing p�y urves. This agrees withanalyti al investigations by Terzaghi(1955), and Vesi (1961). Similarly,Ashford and Juirnarongrit (2005) on luded that initial sti�ness is in-dependent of the pile diameter basedupon an analysis of a �nite elementmodel and tests on large s ale on- rete piles. Carter (1984) and Ling(1988), however, found that the ini-tial sti�ness is linear proportional topile diameter.� Based upon a numeri al model, Lesnyand Wiemann (2006) found that theinitial sti�ness is over-predi ted atlarge depths when onsidering non-slender large-diameter piles.� More resear h is needed regarding theinitial sti�ness of p�y urves.� Fan and Long (2005) found from nu-meri al analyses that the initial sti�-ness of the p�y urves as well as the

ultimate soil resistan e in reases withan in rease in the oe� ient of hor-izontal earth pressure. This e�e t isnot taken into onsideration in the ex-isting p�y urve formulations.� A pile whi h behaves rigidly will havea negative de�e tion at the pile toe ausing shear stresses at the pile toe.Further, pile rotation at the pile toewill impose a moment on the pile aused by verti al stresses a ting onthe pile toe. These e�e ts are nottaken into onsideration in the exist-ing p�y urve formulations.� For non-slender, large-diameter pilesthe resear h regarding the shape ofthe p�y urves is limited.� The p�y urves are developed for ho-mogeneous soils. Few analyses havebeen made on layered soils. Fur-ther these analyses have been on-du ted on �exible piles. Georgiadis(1983) proposed a method to adjustthe p�y urve formulations for layeredsoils in whi h an equivalent depthis determined for the soil layers be-neath the upper layer. M Gann etal. (2012) investigated the e�e t oflayered soil on the p�y urves andfound that both the soil layers aboveand below an intermediate layer af-fe t the p�y urves of the interme-diate layer. Based on the numeri alanalyses M Gann et al. (2012) pro-posed a modi� ation of the p�y urvesdue to layered soil. Both the �ndingsof Georgiadis (1983) and M Gann etal. (2012) needs furhter validationagainst tests on non-slender piles.� Cy li loading is only in a very sim-pli�ed manor in orporated in the ur-rent p�y urve formulations. The a - umulation of pile de�e tion due tolong-term y li loading have been in-vestigated by means of both numer-i al modelling and small-s ale tests.Most resear hers on lude that the

46 pile de�e tion a umulates exponen-tially with the number of y les. Fur-ther, fa tors su h as the relative den-sity, ζb and ζc a�e ts the a umula-tion.� For random y li loading LeBlan etal. (2010b) found that the a umula-tion of pile de�e tion is independentof the loading sequen y, whi h is in ontrast to the �ndings of Peralta andA hmus (2010).� The variation of the sti�ness ofthe soil-pile intera tion with y li loading needs further investigation.LeBlan et al. (2010a) suggestedthat the sti�ness in reases logarith-mi ally with the number of y les in-dependently of the relative density ofthe soil. However, they only onsid-ered piles in loose to medium densesand. Hen e, further investigationsare needed for piles in dense to verydense sand.� For piles installed o�shore withouts our prote tion both global and lo als our will take pla e. This hangesthe soil-pile intera tion. ISO (2007)suggests a simpli�ed method for mod-i� ation of p�y urves due to s our-ing. However, the method needs val-idation. Lin et al. (2010) pointedout that the soil be omes over on-solidated when s ouring takes pla e.Hen e, the oe� ient of horizontalearth pressure and the fri tion anglein reases.� Due to hanging sea onditions thedepth of the s our holes around un-prote ted o�shore piles will vary withtime. Knowledge is needed regardingthe properties of ba k�lled soil mate-rial. Su h knowledge an be essen-tial for optimising the fatigue designfor monopiles designed unprote tedagainst s our development.

Referen esAbdel-Rahman K., and A hmus M., 2005.Finite element modelling of horizontallyloaded Monopile Foundations for O�shoreWind Energy Converters in Germany. In-ternational Symposium on Frontiers inO�shore Geote hni s, Perth, Australia,Sept. 2005.Abdel-Rahman K., and A hmus M., 2006.Numeri al modelling of the ombined axialand lateral loading of verti al piles. Pro- eedings of Numeri al Methods in Geote h-ni al Engineering, Graz, Austria, Sept.2006.A hmus M., and Thieken K., 2006. Be-havior of piles under ombined lateral andaxial loading. 2nd Internaltional Sympo-sium on Frontiers in O�shore Geote hni s,Perth, Australia, Nov. 2010.A hmus M., Abdel-Rahman K., Kuo Y.-S., 2007. Numeri al modelling of largediameter steel piles under monotoni and y li horizontal loading. Pro eedingsof the 10th International Symposium onNumeri al Models in Geome hani s, NU-MOG 10, pp. 453-459.A hmus M., Abdel-Rahman K., andThieken K., 2009a. Behavior of Piles inSand Subje ted to In lined Loads. Pro- eedings of International Symposium onComputational Geome hani s, Juan-Les-Pins, Fran e, May 2009.A hmus M., Kuo Y.-S., and Abdel-Rahman K., 2009b. Behavior of monopilefoundations under y li lateral load.Computers and Geote hni s, 36(5), pp.725-735.A hmus M., Albiker J., and Abdel-Rahman K., 2010a. Investigations onthe behavior of large diameter piles under y li lateral loading. Pro eeding of Fron-tiers in O�shore Geote hni s II, Perth,Western Australia, Australia, pp. 471-476.

47A hmus M., Kuo Y.-S., and Abdel-Rahman K., 2010b. Numeri al Investi-gation of S our E�e t on Lateral Resis-tan e of Windfarm Monopiles. Pro eed-ings of the Twentieth International O�-shore and Polar Engineering Conferen e,Beijing, China, June 2010.A hmus M., and Thieken K., 2010. Be-havior of piles under ombined lateral andaxial loading. Pro eedings of Frontiers inO�shore Geote hni s II, Perth, WesternAustralia, Australia, Nov. 2010, pp. 465-470.Alizadeh M., and Davisson M. T., 1970.Lateral load test on piles - Arkansas Riverproje t. Journal of Soil Me hani s andFoundation Engineering Division, 96(5),pp. 1583-1604.API, 2000. Re ommended pra ti e forplanning, designing, and onstru ting �xedo�shore platforms - Working stress design,API RP2A-WSD, Ameri an Petrolium In-stitute, Washington, D.C., 21. edition.API, 2008. Errata and Supplement 3 for:Re ommended Pra ti e for Planning, De-signing and Constru ting Fixed O�shorePlatforms - Working Stress Design, Ameri- an Petrolium Institute, Washington, D.C.Ashford S. A., and Juirnarongrit T.,Mar h 2003. Evaluation of Pile Dia-meter E�e t on Initial Modulus of Sub-grade Rea tion. Journal of Geote h-ni al and Geoenvironmental Engineering,129(3), pp. 234-242.Ashford S. A., and Juirnarongrit T., 2005.E�e t of Pile Diameter on the Modulus ofSubgrade Rea tion. Report No. SSRP-2001/22, Department of Stru tural En-gineering, University of California, SanDiego.Ashour M., Norris G., and Pilling P., April1998. Lateral loading of a pile in layeredsoil using the strain wedge model. Jour-nal of Geote hni al and Geoenvironmental

Engineering, 124(4), paper no. 16004, pp.303-315.Ashour M., and Norris G., May 2000.Modeling lateral soil-pile response basedon soil-pile intera tion. Journal ofGeote hni al and Geoenvironmental Engi-neering, 126(5), paper no. 19113, pp.420-428.Ashour M., Norris G., and Pilling P., Au-gust 2002. Strain wedge model apa-bility of analyzing behavior of laterallyloaded isolated piles, drilled shafts and pilegroups. Journal of Bridge Engineering,7(4), pp. 245-254.Ashour M., and Norris G., 2003. Lat-eral loaded pile response in lique�able soil,Journal of Geote hni al and Geoenviron-mental Engineering,129(5), pp. 404-414.Banerjee P. K., and Davis T. G., 1978.The behavior of axially and laterallyloaded single piles embedded in non-homogeneous soils. Geote hnique, 28(3),pp. 309-326.Barton Y. O., and Finn W. D. L., 1983.Lateral pile response and p�y urves from entrifuge tests. Pro eedings of the 15thAnnual O�shore Te hnology Conferen e ,Houston, Texas, paper no. OTC 4502, pp.503-508.Belkhir S., Mezazigh S., and Leva her, D.,De ember 1999. Non-Linear Behavior ofLateral-Loaded Pile Taking into A ountthe Shear Stress at the Sand. Geote hni- al Testing Journal, GTJODJ, 22(4), pp.308-316.Bhatta harya S., Lombardi D., and WoodD. M., 2011. Similitude relationships forphysi al modelling of monopile-supportedo�shore wind turbines. InternationalJournal of Physi al Modelling in Geote h-ni s, 11(2), pp. 58-68.Bogard D., and Matlo k H., 1980. Simpli-�ed Cal ulation of p-y Curves for LaterallyLoaded Piles in Sand. Unpublished Report,

48The Earth Te hnology Corporation, In .,Houston, Texas, USA.Briaud J. L., Smith T. D., and Meyer, B.J., 1984. Using pressuremeter urve todesign laterally loaded piles. In Pro eed-ings of the 15th Annual O�shore Te hnol-ogy Conferen e, Houston, Texas, paper no.OTC 4501.Broms B. B., 1964. Lateral resistan eof piles in ohesionless soils. Journal ofSoil Me hani s and Foundation Division,90(3), pp. 123-156.Brødbæk, K. T., Augustesen, A. H.,Møller, M., and Sørensen, S. P. H., 2011.Physi al modelling of large diameter pilesin oarse-grained soil. Pro eedings of the21. European Young Geote hni al Engi-neers' Conferen e (XXI EYGEC), 4.-7.September, Rotterdam, The Netherlands.Budhu M., and Davies T., 1987. Nonlin-ear Analysis of Laterally loaded piles in ohesionless Soils. Canadian geote hni aljournal, 24(2), pp. 289-296.Carter D. P., 1984. A Non-Linear Soil Mo-del for Predi ting Lateral Pile Response.Rep. No. 359, Civil Engineering Dept,.Univ. of Au kland, New Zealand.Comodromos E. M., 2003. Response pre-di tion for horizontally loaded pile groups.Journal of the Southeast Asian Geote hni- al So iety, 34(2), pp. 123-133.Cox W. R., Reese L. C., and Grubbs B. R.,1974. Field Testing of Laterally LoadedPiles in Sand. Pro eedings of the SixthAnnual O�shore Te hnology Conferen e,Houston, Texas, paper no. OTC 2079.Das B. M., Seeley G. R., and Raghu D.,1976. Uplift apa ity of model piles underoblique loads. Journal of the Geote hni alEngineering Division, ASCE, 102(9), pp.1009-1013.Davisson M. T., and Gill L. C., 1963. Lat-erally Loaded Piles in a Layered Soil Sys-tem. Journal of the Soil Meh ani s and

Foundation Engineering Division, ASCE,89(SM3), pp. 63-94.Davisson M. T. and Salley J. R., 1970.Model study of laterally loaded piles.Journal of Soil Me hani s and FoundationEngineering Division, ASCE, 96(5), pp.1605-1627.Desai C. S., Sharma K. G., Wathugala G.W., and Rigby D. B., 1991. Implementa-tion of hierar hi al single surfa e δ0 and δ1models in �nite element pro edure. Inter-national Journal for Numeri al & Analyt-i al Methods in Geome hani s, 15(9), pp.649-680.DNV, 2010. Design of O�shore WindTurbine Stru tures, DNV-OS-J101. DetNorske Veritas, Det Norske Veritas Classi-� ation A/S.Dobry R., Vin ente E., O'Rourke M., andRoesset J., 1982. Sti�ness and Damping ofSingle Piles. Journal of geote hni al engi-neering, 108(3), pp. 439-458.Dordi C. M., 1977. Horizontally LoadedPiles in Layered Soils. Pro eedings of Spe- ialty Session 10, The e�e t of HorizontalLoads on Piles due to Sur harge of Seismi E�e ts, Ninth International Conferen e onSoil Me hani s and Foundation Engineer-ing, Tokyo, Japan, July 1977, pp. 65-70.Dunnavant T. W., and O'Neill M. W.,1985. Performan e analysis and inter-pretation of a lateral load test of a 72-in h-diameter bored pile in over onsoli-dated lay. Report UHCE 85-4, Dept. ofCivil Engineering., University of Houston,Texas, p. 57.Fan C. C., and Long J. H., 2005. As-sessment of existing methods for predi t-ing soil response of laterally loaded pilesin sand. Computers and Geote hni s 32,pp. 274-289.Georgiadis M., 1983. Development of p-y urves for layered soils. Pro eedings of

49the Conferen e on Geote hni al Pra ti e inO�shore Engineering, ASCE, pp. 536-545.Georgiadis M., Anagnostopoulos C., andSa�ekou S., 1992. Centrifugal testing oflaterally loaded piles in sand. CanadianGeote hni al Journal, 29(2), pp. 208-216.Gudehus G., and Hettler A., 1983. ModelStudies of Foundations in Granular Soil, InDevelopment in Soil Meh ani s and Foun-dation Engineering 1, pp. 29-63.Hansen B. J., 1961. The ultimate re-sistan e of rigid piles against transver-sal for es. Danish Geote hni al Institute,Bull. No. 12, Copenhagen, Denmark, 5-9.Harremoës P., Ovesen N. K., and Ja ob-sen H. M., 1984. Lærebog i geoteknik 2, 4.edition, 7. printing. Polyteknisk Forlag,Lyngby, Danmark.Hetenyi M., 1946. Beams on Elasti Foun-dation. Ann Arbor: The University ofMi higan Press.Huurman M., 1996. Development of traf-� indu ed permanent strain in on reteblo k pavements. Heron, 41(1), pp. 29-52.ISO, 2007. Petroleum and natural gas in-dustries - Fixed steel o�shore stru tures.International Organization for Standard-ization, ISO 19902:2007 (E).Jeong S., Kim Y., and Kim J., 2011. In-�uen e on lateral rigidity of o�shore pilesusing proposed p-y urves. O ean Engi-neering, 38(), pp. 397-408.Kagawa T., and Kraft L. M., 1980. Lat-eral load-de�e tion relationships of pilessubje ted to dynami loadings. Soils andFoundations, 20(4), pp. 19-34.Karasev O. V., Talanov G. P., and BendaS. F., 1977. Investigation of the work ofsingle situ- ast piles under di�erent load ombinations. Journal of Soil Me hani sand Foundation Engineering, translatedfrom Russian, 14(3), pp. 173-177.

Karthigeyan S., Ramakrishna V. V. G. S.T., and Rajagopal K., May 2006. In�u-en e of verti al load on the lateral responseof piles in sand. Computers and Geote h-ni s 33, pp. 121-131.Khadilkar B. S., Chandrasekaran V. S.,and Rizvi I. A., 1973. Analysis of LaterallyLoaded Piles in Two-Layered Soils. Pro- eedings of the Eigth International Con-feren e on Soil Me hani s and FoundationEngineering, Mos ow, Russia, pp. 155-158.Kim Y., and Jeong S., 2011. Analysisof soil resistan e on laterally loaded pilesbased on 3D soil-pile intera tion. Comput-ers and Geote hni s, 38(2), pp. 248-257.Klinkvort R. T., and Hededal O., 2010.Centrifuge modelling of o�shore monopilefoundations, Pro eedings of InternationalSymposium Frontiers in O�shore Geote h-ni s 2, Perth, Western Australia, Novem-ber 8 to November 10 2010.Kuo Y.-S., 2008. On the behavior of large-diameter piles under y li lateral load,Ph.D. thesis Vol. 65, Leibniz UniversityHannover, Hannover, Germany.LeBlan C., 2009. Design of o�shore windturbine support stru tures: Sele ted top-i s in the �eld of geote hni al engineer-ing, DCE Thesis, Department of Civil En-gineering, Aalborg University, Denmark,(18).LeBlan C., Houlsby G. T., and Byrne B.W., 2010a. Response of Sti� Piles to Long-term Cy li Loading, Geote hnique, 60(2),pp. 79-90.LeBlan C., Houlsby G. T., and ByrneB. W., 2010b. Response of sti� piles torandom two-way lateral loading, Geote h-nique, 60(9), pp. 715-721.Lesny K., and Wiemann J., 2006. Finite-Element-Modelling of Large DiameterMonopiles for O�shore Wind Energy Con-verters. Geo Congress 2006, February 26

50to Mar h 1, Atlanta, GA, USA.Lesny K., and Hinz P., 2007. Investigationof monopile behaviour under y li lateralloading. Pro eedings of O�shore Site In-vestigation and Geote hni s, London, Eng-land, pp. 383-390.Lesny K., Paikowsky S. G., and GurbuzA., 2007. S ale e�e ts in lateral load re-sponse of large diameter monopiles. Geo-Denver 2007 February 18 to 21, Denver,USA.Lesny K., and Hinz P., 2009. Contempo-rary Topi s in Deep Foundations - Pro- eedings of sele ted papers of the 2009International Foundation Congress andEquipment Expo, pp. 512-519.Lin S.-S., and Liao J.C., 1999. Per-manent Strains of Piles in Sand due toCy li Lateral Loads, Journal of Geote h-ni al and Geoenvironmental Engineering,125(9), pp. 798-802.Lin C., Bennett C., Han J., and ParsonsR. L., 2010. S our e�e ts on the responseof laterally loaded piles onsidering stresshistory of sand, Computers and Geote h-ni s, 37, pp. 1008-1014.Ling L. F., 1988. Ba k Analysis of Lat-eral Load Test on Piles. Rep. No. 460,Civil Engineering Dept., Univ. of Au k-land, New Zealand.Little R. L., and Briaud J. L., 1988a.Cy li Horizontal Load Test on 6 Piles inSands at Houston Ship Channel. Resear hReport 6540 to USAE Waterways Exper-iment Station, Civil Engineering, A&MUniversity, Texas, USA.Little R. L., and Briaud J. L., 1988b. Fulls ale y li lateral load tests on six sin-gle piles in sand. Mis ellaneous Paper GL-88-27, Geote hni al Division, Texas A&MUniversity, College Station, Texas, USA.Long J. H., and Vanneste G., 1994. Ef-fe ts of Cy li Lateral Loads on Piles in

Sand. Journal of Geote hni al Engineer-ing, 120(1), pp. 225-244.Matlo k H., and Reese L. C., 1960. Gener-alized Solutions for Laterally Loaded Piles.Journal of the Soil Me hani s and Foun-dations Division, 86(5), pp. 63-91.Matlo k H., 1970. Correlations for De-sign of Laterally Loaded Piles in SoftClay. Pro eedings, Se ond Annual O�-shore Te hnology Conferen e, Houston,Texas, paper no. OTC 1204, pp. 577-594.M Clelland B., and Fo ht J. A. Jr., 1958.Soil Modulus for Laterally Loaded Piles.Transa tions. ASCE 123: pp. 1049-1086.M Gann C. R., Arduino P., andMa kenzie-Helnwein P. (2012). Sim-pli�ed Pro edure to A ount for a WeakerSoil Layer in Lateral Load Analysis ofSingle Piles. Journal of Geote hni al andGeoenvironmental Engineering, ASCE,a epted De ember 14. 2011, postedahead of print De ember 17 2011.Meyerhof G. G., Mathur S. K., and Val-sangkar A. J., 1981. Lateral resistan e andde�e tion of rigid wall and piles in layeredsoils, Canadian Geote hni al Journal, 18,pp. 159-170.Meyerhof G. G., and Sastry V. V. R. N.,1985. Bearing apa ity of rigid piles un-der e entri and in lined loads. CanadianGeote hni al Journal, (22), pp. 267-276.Miner M. A., 1945. Cumulative Damagein Fatigue. Journal of Applied Me hani s,12, pp.A159-A164.Mur hison J. M., and O'Neill M. W, 1984.Evaluation of p�y relationships in ohe-sionless soils. Analysis and Design of PileFoundations. Pro eedings of a Symposiumin onjun tion with the ASCE NationalConvention, pp. 174-191.Naik T. R., and Peyrot A., 1976. Analysisand Design of Laterally Loaded Piles andCaissons in a Layered Soil System. Meth-ods of Stru tural Analysis, Pro eedings of

51the National Stru tural Engineering Con-feren e, ASCE, Madison, Wis onsin, USA,Aug. 1976, pp. 589-606.Norris G. M., 1986. Theoreti ally basedBEF laterally loaded pile analysis. Pro- eedings, Third Int. Conf. on Numeri alMethods in o�shore piling, Editions Te h-nip, Paris, Fran e, pp. 361-386.O'Neill M. W., Mur hison J. M., 1983. AnEvaluation of p-y Relationships in Sands.Resear h Report No. GT-DF02-83, De-partment of Civil Engineering, Universityof Houston, Houston, Texas, USA.O'Neill M. W., and Dunnavant T. W.,1984. A study of e�e t of s ale, ve-lo ity, and y li degradability on later-ally loaded single piles in over onsolidated lay. Report UHCE 84-7, Dept. of Civ.Engrg., University of Houston, Texas, p.368.Pasternak P. L., 1954. On a New Methodof Analysis of an Elasti Foundation byMeans of Two Foundation Constants, Go-sudarstvennoe Izadatelstro Liberatuni poStroitelstvui Arkhitekture, Moskow, pp.355-421.Pe k R. B., Hanson W. E., and Thorn-burn T. H., 1953. Foundation Engineer-ing, John Wiley and Sons, In . New York.Pender M. J., 1993. Aseismi Pile Foun-dation Design Analysis. Bull. NZ Nat.So . Earthquake Engineering., 26(1), pp.49-160.Pender J. M., Carter D. P., and Pran-joto S., 2007. Diameter E�e ts on PileHead Lateral Sti�ness and Site Investiga-tion Requirements for Pile Foundation De-sign. Journal of Earthquake Engineering,11(SUPPL. 1), pp. 1-12.Peng J.-R., Clarke B. G., and RouainiaM., 2006. A Devi e to Cy li LateralLoaded Model Piles, Geote hni al TestingJournal, 29(4), pp. 1-7.

Peralta P., and A hmus M., 2010. An ex-perimental investigation of piles in sandsubje ted to lateral y li loads, Physi alModelling in Geote hni s, Taylor& Fran isGroup, London.Petrosowit h G., and Award A., 1972. Ul-timate lateral resistan e of a rigid pile in ohesionless soil, Pro eedings of the 5thEuropean Conferen e on SMFE, Madrid,3, pp. 407-412.PHRI, 1980. Port and Harbour Resear hInstitute. Te hni al Standards for Portand Harbour Fa ilities in Japan., O� eof Ports and Harbours, Ministry of Trans-port.Poulos H. G., 1971. Behavior of laterallyloaded piles: I - Single piles. Journal of theSoil Me hani s and Foundations Division,97(5), pp. 711-731.Poulos H. G., and Davis E. H., 1980. Pilefoundation analysis and design, John Wi-ley & Sons.Poulus H., and Hull T., 1989. The Roleof Analyti al Geome hani s in FoundationEngineering. Foundation Eng.: Currentprin iples and Pra ti es, 2, pp. 1578-1606.Prakash S., 1962. Behavior of pile groupssubje ted to lateral loads. Thesis, Univer-sity of Illinois, Urbana, Illinois, USA.Prasad Y. V. S. N., and Chari T. R., 1999.Lateral apa ity of model rigid piles in ohesionless soils, Soils and Foundations,39(2), pp. 21-29.Reese L. C., and Matlo k H., 1956.Non-dimensional Solutions for LaterallyLoaded Piles with Soil Modulus AssumedProportional to Depth. Pro eedings of theeighth Texas onferen e on soil me hani sand foundation engineering. Spe ial pub-li ation no. 29.Reese L. C., Cox W. R., and Koop, F. D.,1974. Analysis of Laterally Loaded Pilesin Sand. Pro eedings of the Sixth Annual

52O�shore Te hnology Conferen e, Houston,Texas, 2, paper no. OTC 2080.Reese L. C., and Wel h R. C., 1975. Lat-eral loading of deep foundation in sti� lay.Journal of Geote hni Engineering., Div.,101(7), pp. 633-649.Reese L. C., and Van Impe W. F., 2001.Single Piles and Pile Groups Under Lat-eral Loading, Taylor & Fran is Group pl ,London.Remaud D., Garnier J., and Frank R.(1998). Laterally loaded piles in densesand - group e�e ts. Pro eedings of the In-ternational Conferen e Centrifuge, Tokyo,Japan, pp. 533-538.Ry klik I., 1987. A new de�nition of therain�ow y le ounting method. Interna-tional Journal of Fatigue, 9(2), pp. 119-121.S ott R. F., 1980. Analysis of CentrifugePile Tests: Simulation of Pile Driving. Re-sear h Report, Ameri an Petroleum Insti-tute OSAPR Proje t 13, California Insti-tute of Te hnology, Pasedena, California,USA.Stevens J. B., and Audibert J. M. E.,1979. Re-examination of p-y urve for-mulation. Pro eedings Of the XI AnnualO�shore Te hnology Conferen e, Houston,Texas, OTC 3402, pp. 397-403.Stewart H. E., 1986. Permanentstrains from y li variable-amplitudeloadings. Journal of Geote hni al Engi-neering, ASCE, 112(6), pp. 646-661.Sørensen, S. P. H., Brødbæk, K. T.,Møller, M., Augustesen, A. H., and Ib-sen, L. B., 2009. Evaluation of Load-Displa ement Relationships for Large-Diameter Piles. Pro eedings of thetwelft International Conferen e on Civil,Stru tural and Environmental EngineeringComputing (eds. Topping, Costa Nevesand Barros), 1.-4. September, Madeira,Portugal, paper 244.

Sørensen, S. P. H., Ibsen, L. B., and Au-gustesen, A. H., 2010. E�e ts of diameteron initial sti�ness of p�y urves for large-diameter piles in sand. Pro eedings ofthe seventh European Conferen e on Nu-meri al Methods in Geote hni al Engineer-ing (eds Benz &Nordal eds), 2.-4. June,Trondheim, Norway, pp. 907-912Terashi M., 1989. Centrifuge modeling ofa laterally loaded pile. Pro eedings of theTwelfth International Conferen e of SoilMe hani s and Foundation Engineering,Rio de Janeiro, Brazil, pp. 991-994.Terzaghi K., 1955. Evaluation of oe�- ients of subgrade rea tion. Geote hnique,5(4), pp. 297-326.Timoshenko S. P., 1941. Strength of ma-terials, part II, advan ed theory and prob-lems, 2nd edition, 10th printing. NewYork: D. Van Nostrand.Verdue L., Garnier J., and Leva her D.,2003. Lateral y li loading of single pilesin sand. International Journal of Physi alModelling in Geote hni s, 3(3), pp. 17-28.Vesi A. S., 1961. Beam on Elasti Sub-grade and the Winkler's Hypothesis. Pro- eedings of the 5th International Confer-en e on Soil Me hani s and FoundationEngineering, Paris, 1, pp. 845-850.Winkler E., 1867. Die lehre von elasti zi-tat and festigkeit (on elasti ity and �xity),Prague, 182 p.Yang Z., and Jeremi B. (2005). Studyof Soil Layering E�e ts on Lateral Load-ing Behavior of Piles. Journal of Geote h-ni al and Geoenvironmental Engineering,ASCE, 131(6), pp. 762-770.Zhang L., Silva F., and Grismala R., Jan-uary 2005. Ultimate Lateral Resistan eto Piles in Cohesionless Soils. Journal ofGeote hni al and Geoenvironmental Engi-neering, 131(1), pp. 78-83.

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ISSN 1901-726X DCE Technical Report No. 137